I voted for Sony to make one. Microsoft REALLY needs to focus on their content, and adding a handheld console into the mix is just going to cause more fragmentation that - in my opinion - would damage their output. This has nothing to do with Microsoft not being able to develop a handheld console (although they have never tried, so who knows if they can or not), and everything to do with not stretching themselves too thin and damaging their brand/reputation by trying to have their eggs in too many baskets.
On the other hand, Sony has already tested the handheld market. It knows how to create a handheld console, and they are large enough that they can take some risks and attempt to develop a handheld console that can invade Nintendo's space. Having Sony split their focus on two fronts (one going up against Microsoft, and the other going up against Nintendo) would probably even help all three console makers.
Microsoft would have some room to breath and focus on building up the quality of their studio output since Sony wouldn't be focused solely on Microsoft. Nintendo would need to put a bit more effort into subsequent handhelds since Sony could, and, in this alternate reality where this is happening, likely would, outclass Nintendo in terms of hardware. While that sounds like a downside for Nintendo, it's actually a positive as it keeps Nintendo from becoming stagnant or coasting off of past successes, and there are plenty of people who would be thrilled to see Nintendo increasing the quality of their handheld consoles. Sony would open themselves to a broader market of mobile gamers who still want a handheld device instead of a cell phone.
