I'm breaking rule #1, because there's no way I can have a video recorded, uploaded, and annotated by 3 days ago.
1.- Best Game play
MM3, hands down. Both require precise movements to be successful, yes. But the updated physics in MM3, and the added depth of sliding and the Rush Adaptors make it more possible in 3; though 2 does get props for some unique elements, like the Buebeam Trap and concept of QuickMan's level; even if a little unbalanced in concept (BBT: blow it once, and you're screwed for good!).
2.- Best Robot Masters (compare the 8 robot masters from each game)
Duh. MM3 features all sixteen.
3.- Best Weapons (compare the weapons of both games and give your toughts)
TIE. Every weapon has it's usefulness, even if Spark Shock's is just MagnetMan. Even Shadow Blade ultimately makes sense, as ShadowMan is an amalgomation of QuickMan and MetalMan, and Shadow Blade is one of Quick Boomerang and Metal Blade.
4.- Best Design
Apples and oranges. MM2's plot is supplanted as it's opening and ending, while 3's gameplay IS the plot (though badly illustrated/not clarified.) MM7 is like a midpoint in design that, applied to either of these titles, would be maserful.
5.- Best Soundtrack
MM2, hands down, practically DEFINED the MegaMan sound, all around. MM3's soundtrack was great, but a little more hit-or-miss in some departments; most notably the use and appropriate level of percussion.
6.- Best Ideas
MM3. Not only with Rush and the slide, but the unforgettable concept of the Doc Robot levels; a key ingredient in the MM3 masterpiece that has yet to be reproduced in any of it's following titles. Another example is it's use of widgets; the magnets in MagnetMan's stage produced an anomaly in the gameplay that made such a level seem impossible to navigate otherwise.
7.- Best Game
MM3, but such a concept would never exist if MM2 hadn't existed first, AND been such a blockbuster to begin with.