The AIM9X is a very different missile from the Sidewinder's predecessors.  The only thing in common is the rocket motor and the aircraft interface.  Everything else has changed.

The seeker is far far superior with a very high field of regard and much higher field of view than previous Sidewinders, permitting very high off bore-sight shots.  The seeker can also be slaved to an aircraft cuing system (radar, helmet sight, HUD) to enable lock-on before leaving the rail while highly off bore sight.  The seeker is much more sensitive for greater acquisition and lock-on ranges and is much more resistant to countermeasures.  The airframe is much more agile with an improved autopilot and thrust vectoring, with the ariframe and autopilot able to handle higher G maneuvers, and the autopilot having improved intercept algorithms.

The AIM9X can use existing Sidewinder rocket motors, saving LOTS of money because there are literally thousands and thousands of Sidewinders around.   However, an improved rocket motor can also be fitted, which, with the much longer range seeker, can make the Sidewinder a near Beyond Visual Range weapon.

The warhead is improved, but that's almost a side issue.  The improved seeker, guidance system and flight controls means a high probability of a hit-to-kill intercept.  It has a proximity fuse in case it misses, but it's probably going to actually hit the target and explode rather than exploding nearby and depending on shrapnel to make the kill.