Mr. Mehta:
In one sense, you are "comparing apples to oranges," for the Dragunov is not exactly a sniper rifle, to which you are comparing it.
However, regarding cartridges: as Jonah notes, the .30-'06 was replaced in the USA's arsenal by the .308, or 7.62x51. The 7.62x51 is a shortened version of the .30-06; its purpose was to permit the same ballistics in a shorter round, which, in turn, would allow shorter and more efficient automatic weapons -- both machine guns and shoulder arms.
The smaller capacity case of the .308 achieved this by using more modern propellents, notably Olin's (Olin was Winchester's parent company and a chemical company, like DuPont) then-new "ball powder." When comparing smaller cases with larger cases, when operating at the same pressures, the smaller case will generally come closest to matching the performance of the larger case with lighter bullets. It is with the heavier bullets that the larger case will usually show the larger advantage.
You mention a 200 fps velocity difference between the .30-'06 and the .308: that much variance can be encountered with the same round in different kinds of rifles. It is not that much of a difference.
Please note that the case capacity and performance of the 7.62x54r cartridge that was originally used by the Tsarist Russian army and is also used in the Dragunov over 100 years later comes pretty close to the .308's performance. Also note that the whole US effort to obtain a battle rifle to replace the .30-40 Krag amounted to a lot of copying from the M98 Mauser -- enough of a copy that, when the rifle came out, the USA had to pay royalties to Mauser for patent infringements. In the areas where the USA didn't copy from Mauser, some of those "improvements" turned out to be less capable than the original Mauser design.
The .30-'06 cartridge was the USA's "improvement" of the 7.92x57 (8mm) round, and as such, did not offer any great improvement in performance and was longer, requiring a longer action to handle it. The .308 was, in essence, a recognition and correction of this choice: A realization that the job needing to be done was better addressed with a shorter cartridge.
This said, the .30-'06 has proven to be a very popular round, as its case capacity allows a lot of variations in loads. For the military, this is not so important: the military is not using the cartridge to hunt everything from ground squirrels to elephants.
The gist of what I've said so far is that, for the intended purpose of a sniper rifle, the old 7.62x54r round's performance compares quite well with the .308 (7.62x51) round the USA currently uses -- the one the USA chose to replace the .30-'06.
I would also note here that the calibration of sights, 1300m for the 7.62x54r and 2300m for the .30-'06 is not to be taken as an indication of the ranges these two cartridges are capable of driving tacks: closely clustered groups required for effective sniping. Rather, the 1300m sighting is a range that one might reasonably expect as maximum for sniping with the 7.62x54r. 2300m is the range that would be used back in the WW1 era for "Volley Fire," where troops would lay down a long range fire similar to yeoman archers laying down a covering fire of arrows at Agincourt. Such "Volley Fire" is no longer used in the military. You can see an example of this in the SMLE rifle used by Indian forces and chambered in 7.62x51: the originals used the volley fire 2000m calibrated sights inherited from the SMLE No.1 Mk III days, but the Indian 2A1 modification had limited range calibration only out to 800m,
but still using the same cartridge and practically the same rifle.
I suggest that the calibration of the sights you are quoting as a reference to the potency of the cartridge has much more to do with the use each rifle was intended to be put to on the battlefield.
Now, regarding the rifle; the Dragunov vs. some bolt action rifle, then the comparison is also shaded by military, as opposed to hunting and sporting, considerations. The USA has used both M70 Winchester and M700 Remington bolt action sniper rifles.
Here, I would note that the use of a hunting rifle as a sniper weapon has some ramifications. A number of measures are taken to adapt a commercially available hunting rifle for military use -- the US forces don't just go down to the local WalMart and buy a M700 with a Leupold scope and head out to the battlefield with it.
The Soviets, on the other hand, have a very long history of sniping, and have spent many years developing it. There is some divergence here between the US and the Soviet practice.
The USA, after WW2, practically dropped its sniper program that it had developed from scratch during that war. During the Korean conflict and Vietnam, the USA had to restart sniper development again.
The Soviet Union, however, paid a great deal of attention to sniping and used snipers as an integral part of their battlefield tactics. One of these tactics was to leave snipers in place behind when their main forces retreated, which allowed their snipers to open fire on the enemy's back when counterattacks were made. Their tactics called for large numbers of snipers and which, therefore, required a great number of sniper rifles.
While the USA, even in the design of the M1903 Springfield, stressed individual marksmanship (The M1903 Springfield was rightly renowned for its inherent accuracy, mainly due to the more effective bedding the receiver design permitted, as compared to the M98 Mauser), The Russians in Tsarist days saw the rifle as a support for their main weapon: the bayonet, used in massed infantry charges.
Thus, the Mosin Nagant rifle was much simpler and, to some eyes, more crude than either the M1903 Springfield or the M98 Mauser.
However, the old saw that has been quoted on this site before is true and should be kept in mind: The Germans used the best sporting rifle (M98), the British used the best battle rifle (SMLE), and the USA used the best target rifle (M1903). The Russians used the Mosin Nagant for all 3 purposes.
Keep in mind that target rifles based on the Mosin Nagant receiver continued to be used in and win in competition by the Soviet Union and Finland long after WW2!
http://en.wikipedia.org/wiki/7.62_Tkiv_85
Anyway, the Soviets in WW2 did not use special match grade Springfields for their snipers; they used M91-30 Mosin Nagants taken right from the assembly lines. Rifles that proved exceptionally accurate were selected for sniper use and fitted with scope sights. When the rifles lost their sniper accuracy, they were often returned to front line troop use.
The point I wish to illustrate here is that the US doctrine comes from a nation of marksmen that sees sniping as a small, elite corps, fitted with specialized weapons. The Soviet doctrine saw sniping as an extension of its massive army, equipped with weapons that were much more like what the front line troops carried.
In addition to this, the Dragunov was not intended for the same sort of specialized sniper use that the USA uses modified bolt action hunting rifles for. Refer to this wiki:
http://en.wikipedia.org/wiki/Dragunov_sniper_rifle
The Dragunov was designed as a squad support weapon, since according to Soviet and Soviet-derived military doctrines the long-range engagement ability was lost to ordinary troops when submachine guns and assault rifles (which are optimized for close-range and medium-range, rapid-fire combat) were adopted.
For this kind of duty, more firepower than a bolt action hunting rifle is called for. A semi-automatic weapon is more desirable for long range squad support.
So, I would reply to your question by saying that the Indian Army's use of the Dragunov, rather than some bolt action weapon, may be more suitable for the tactical situations that the military doctrine specifies them to be deployed in.
To put this another way, please consider the final part of the wiki on the Dragunov:
The Dragunov is an original rifle design for several reasons. First, it was not meant for highly trained and specialized sniper teams, but rather for designated marksmen, spread in every basic infantry unit. In every platoon of Warsaw Pact troops, there was a Dragunov rifle marksman. In the German Democratic Republic arsenals alone, there were almost 2,000 Dragunov rifles,[10] while in many Western armies there was not even a single sniper rifle except in special forces units (as example, in the Italian Army until the 1990s), but in Warsaw Pact troop formations, the Dragunov marksmen were widespread among the regular units. To fulfill this role the rifle is relatively light for a sniper rifle but well balanced, making it easier to use in a dynamic battle. It also is a semi-automatic rifle, a rare feature for accuracy oriented rifles in the 1960s (except for customized ordnance, like M1 Garands), to allow rapid fire and quicker engagement of multiple targets. In order to fire effective API ammunition, its accuracy potential was slightly downgraded by shortening the twist rate, another uncommon priority for a pure sniper rifle. Its precision is good but not exceptional, also because it has a relatively light barrel profile. Like an assault rifle, the rifle has mounts on the barrel to fix a bayonet. The standard AKM bayonet can even be used to cut barbed wire. Lastly, the rifle was meant to be a relatively cheap mass produced firearm.
These features and unusual characteristics were driven by the tactical use doctrine of Dragunov armed marksman which was; from (just behind) the first line targeting high value targets of opportunity and providing special long-distance disrupting and suppressive fire on the battlefield, even with sudden close encounters with enemy troops in mind. A relatively small number of marksman could assist conventional troops by combating or harassing valuable targets and assets such as: enemy key personnel like officers, non-commissioned officers and radio operators, exposed tank commanders, designated marksman and snipers, machinegun teams, anti-tank warfare teams, etc.