I would take the Viewsonic Pro 8200 over the w1200 and HD20 for most peoples uses, especially if you are a gamer. The Viewsonic is the better gaming projector over the other two, the Benq is slightly better at movies because of better blacks. Make sure the Viewsonic will fit in your room, it has a large offset.
The Viewsonic Pro8200 has almost zero gaming lag, the w1200 is nearly unuseable in games 100+ms lag. The Viewsonic is an exceptional NON-3D gaming projector, it will beat the 720p units in gaming. IMHO, the Viewsonic even beats the Epson 8350 in gaming and bright scenes and sharpness. I personally prefer the image of the Viewsonic over the Epson LCD image even for most movies, because the Viewsonic produces a more film-like image than the Epson due to a higher pixel fill ratio of DLP. Sure, SDE is not an issue at 1080p for most, but it still affects the smoothness of the image. People pay thousands for e-shift of the RS-55, and that is going even beyond the pixel fill simulation of DLP (much less LCD), so it shows you it still does matter.
Both the Benq and Viewsonic are about the same brightness. The Viewsonic has less rainbow effect if you are sensitive, even most people sensitive to RBE would find the Viewsonic to not be bothersome. I have owned a few different DLP's including the Mitsubishi hc4000, and other than the 6x color wheels of the Optoma hd33, the Pro8200 is the only one that doesn't have much rainbow effect under $1500 for me. I can spot one on a very rare occassion, but on a Mits or Benq DLP (which also have 4x color wheels), I can see them almost constantly in dark games or movies, but not on the Viewsonic. It is a 7 segment instead of a 6 segment wheel even though they all run at 4x, and this seems to make a huge difference.
That is why I still own the Viewsonic instead of other DLP's, because of almost zero RBE and zero LAG. Many of the 720p projectors only have 3x color wheels, and that is more RBE than even a Mits or Benq, much less the Viewsonic which has almost none. So the 720p DLP's have WAY too much RBE if you are sensitive (keep in mind most people aren't that sensitive to rainbows, but a good number are at 3x speed wheels).
I have over 1000 lamp hours on the Viewsonic with zero issues and the lamp is still VERY bright since the projector starts out so bright. I also own the JVC RS-45, and honestly unless I'm watching a movie with a ton of dark scenes, then I have no problem using the Viewsonic instead of the JVC to keep the lamp hours low on the JVC. I cannot say the same about other projectors I have owned. The Viewsonic is easily the best all-around DLP projector ever made under $1000 when you average it all the attributes out (gaming, brightness, sharpness, etc...). I also really like the Mits hc4000, but the problem with it was too much RBE for me and not enough brightness. The Viewsonic solves both and at a lower price, and the black levels are suprisingly close to the Benq w1200 (not quite as good).