Modern Warfare III has the better multiplayer; Modern Warfare II has the better campaign. MWIII shipped with remastered MW2 (2009) maps and faster movement that the community preferred. MWII's campaign is the more ambitious of the two and its Special Ops missions are stronger.
Same engine and same core feel, and progression carries between them, which blurs the line considerably.
The map pool is the strongest in years because it is largely a remaster of a classic one, and the movement changes made it quicker.
More varied missions and a stronger set-piece run. If multiplayer is not the point for you, this is the better single purchase.
Modern Warfare III has the better multiplayer; Modern Warfare II has the better campaign. MWIII shipped with remastered MW2 (2009) maps and faster movement that the community preferred. MWII's campaign is the more ambitious of the two and its Special Ops missions are stronger.
Better is the wrong question for these two — they are close enough that the answer depends on what you want from the next twenty hours. Pick Modern Warfare III for multiplayer. Pick Modern Warfare II for the campaign.
No. There are no scores anywhere on this page. This is a written opinion about what each game is for, so you can judge whether it matches what you are after.