Bell Helicopter's entry into this competition is more of an incremental upgrade to their V-22 tiltrotor technology: http://bellv280.com/ The Army also wants something smaller than the V-22 (the V280 will end up being probably 1/3 to 1/2 the size) and it will presumably be correspondingly cheaper per aircraft. (Of course with the way these programs usually turn out, who knows how much budget overrun it'll see...)
Karem Aircraft is also proposing a tiltrotor, and is partnering with Lockheed, though I don't think either has experience with tiltrotors.
Sikorsky and Boeing teamed up to build an upgraded version of the X2.
Interestingly, AVX also has a lot of former V-22 engineers and management working for them, so they may have had their reasons for opting against a tiltrotor arrangement, such as a simpler drive and control system.
Personally though, I'd bet that either the Bell or Sikorsky/Boeing proposal will get selected, simply because they've had experience with comparable aircraft, which will give them a better handle on the estimated performance, rather than just making paper helicopters. They're also the big names in US military rotorcraft, and currently have the facilities to ramp up to that kind of production (4000 helicopters is a helluva lot of aircraft).