If Microsoft made a handheld, what do you think would happen? I don't think it would be successful. I think Microsoft would make the same mistake Sony did with console-like games on handhelds. It would be more successful than Vita thought, since I think Halo and the other ones would sell more than Uncharted, and there would be more marketing.
There is no mistake with "console-like" games on the Vita. Those games sell quite well. The Vita also has an absolute ton of smaller games, which strangely seems to be glossed over often. Even beyond that, ANY game is handheld-ready when you can instantly pause and resume at any point.
That argument is still bad and needs to die.
No, the Vita isn't doing well because Sony places almost no emphasis on first-party hand-held development. They left that to third-parties, which simply does not work. They have no major exclusive franchises created in-house to boost sales and they have very few titles aimed specifically at children, which is the main audience in the west. Social games are the big sellers in Japan, another genre which the Vita lacks. It's not that the Vita has "console-like" games--the 3DS has those, too--it's that they have way too few big games, period.
Which is probably what would happen with a Microsoft hand-held. They would have to dedicate an vast amount of resources to creating content, which I just don't see happening, never mind that Japan would ignore the device, taking away a huge market for hand-helds.
No, Microsoft isn't going to make the mistake of trying to break into that market. They'd get into mobile gaming long before they would even consider dedicated hand-held gaming machines.