The question is simple. Will an XBOX (or if Microsoft changes their console brand, a future Microsoft console) ever outsell a future Nintendo handheld (or smartphone if they venture down that alley)?

The 360 will outsell the 3DS by the time the 3DS is done selling. Or do you mean in the same generation?

Are you only comparing two systems within the same generation or can we compare cross-generation? That is, can I compare the X360 to the 3DS?

They have to be the same gen

If its per generation wize, (Like x1 vs 3ds) then no but if its like 360 vs 3ds, then maybe

Put that in the OP considering three people had to ask.

Also, not this generation, no. Next generation? How the hell can I predict that? I guess it can happen.

Xbox 360 > 3DS

There's no way. Nintendo's handhelds always sell huge numbers.

Gameboy+Color: 120M
Gameboy Advance: 80M
DS: 150M
3DS: 45M*

*3DS is not done selling, obviously.

Basically, 80 million is the minimum, about the same number the Xbox 360 sold. And I honestly don't see the Xbox One, or even the PS4, selling that much over lifetime.

Considering everything Nintendo is on the decline lately, maybe next gen. But since when did Nintendo handhelds and Xboxes start competing? I'm still waiting for you to acknowledge this thread you made:
http://gamrconnect.vgchartz.com/thread.php?id=189528&page=1#

You don't see PS4 doing 80 million........ 

And I think 80 million on 3DS might be overstating it; calling it a minimum.