It appears that the upgrades involve significant changes (paid subscription required):

The upgraded R-77 is both heavier and longer than the basic missile. It weighs 190 kg. (418 lb.) rather than 175 kg., and is 3.71 meters (12.17 ft.), rather than 3.6 meters, in length, according to company data.

The increased range is at least in part due to improved aerodynamics. A company executive says the radome shape has been refined, while a “boat-tail” configuration has been introduced at the rear to help drag reduction. Adapting the missile to fly lofted trajectories would also increase the maximum launch range. The executive adds that the active radar seeker has been improved. The manufacture of the RVV-SD seeker is believed to still be Istok.

It also looks like they may be moving away from the unique lattice fins, so as to improve range, at the cost of a slight loss of agility, and the need for larger actuators to move these surfaces.

Considering that the IR guided R-73 (AA-11 Archer) already out ranges the Sidewinder for dogfight applications, this may be a reasonable trade-off.

A further development of the basic R-77 design, previously associated with the Article 180 designation, is also underway, though manufacturer TRV remains unwilling to discuss the program. It is likely that the missile’s signature lattice fins have been replaced with a conventional design, with further range improvements included. This is possibly based on the introduction of a dual-, rather than a single-pulse, solid-rocket motor.

With a weight of 190 kg, as opposed to the 152 kg, physics would seem to dictate that it would have superior range and terminal energy to the AIM-120 AMRAAM, even with the “egg crate” fins.

The use of a lofted trajectory may very well be something that can be retro-fitted through software, which might allow for significant improvements in range for the existing inventory.

I will suggest that this story seems to indicate that reports of a ramjet powered R-77M1 on Wiki are premature.