I just want to know which is better option or which other it recomended but under 800dls.
sorry for my english, I hope I have given to understand
They all have trade-offs. I owned/own the Mits hc4000 and Pro8200 and tried the other two as well.
The w1200 is NOT a gaming projector because of severe lag, and I believe the Optoma hd20 has very LOW lag. You could also look at the Pro8200 (it's very similar to the Optoma, but it's brighter and has less RBE just in case you are RBE-sensitive). The Pro8200 has the least lag for gaming (<20ms) and is the brightest, but it's not as sharp as the Benq w1200 or the Mits hc4000 (it's VERY close to the Mits though, because the VS has better focus uniformity). However, the VS Pro8200 does have a VERY minor 1:1 pixel mapping only around the borders of images (undefeatable edge enhancement). The Benq w1200 was also reported to have an "undefeatable edge enhancement" by at least one reviewer, but when I saw it in person I could not tell and it looked sharper to me than the others.
The blacks on the Pro8200 or the hd20 are not presumably as good as the other two PJ's (but I couldn't tell how good/bad the blacks on the w1200 really were as it wasn't in a dedicated dark room - it was in a semi-dark room). So another one to consider is the Mits hc4000, it has no real lag to speak of, but it's just not as bright as the w1200 or Viewsonic (Mits about same brightness as the hd20 though). The Mits hc4000 has some neat features like the ability to do CIH / 2.35 format screens and switch back and forth automatically, something none of these other three projectors have.
The below should help (>= means it depends really what attribute you value, or too close to call, but the projector on the > side is likely to be VERY slightly better).
For Movies: (black levels, cleanliness, features)
Mits hc4000 > Benq w1200 > Pro8200 >= HD20
For Sports and General TV (features, motion, cleanliness)
Benq w1200 (FI + 120hz) >= Mits hc4000 (cleaner native motion at 60hz though) > HD20 >= Pro8200
For Gaming (lag and other factors in gaming)
Pro8200 > Mits hc4000 > HD 20 > Benq w1200
For Brightness or Ambient Light
Pro8200 > Benq w1200 > HD 20 and Mits hc4000 (about the same brightness)
Benq w1200 > Mits hc4000 > Pro82000 =?? hd20
(hd20 does 1:1 pixel mapping without edge errors, but the VS has better focus uniformity, it's a toss up from what I saw)
For Color (OOTB Pre-Calibration)
Mits hc4000 > Pro82000 > w1200 > hd20
For Color (After Calibration)
Mits hc4000 and w1200 > Pro8200 and hd20
Least Amount of DLP Rainbow Effect
Pro8200 > hd20 > Mits hc4000 and w1200