I'll give my personal opinions about both cars.
Looks wise, that is all subjective. Neither are very "manly" to begin with, but it doesn't bother me at all. You either love the cars, or hate them.
Honestly, I like the fact I can drive around and not see very many Miatas. I MIGHT see another once a day on the way to/from work. On a Civic and such, you see at least 2-3 at every stoplight. and that would bother me. Fortunately, you're good to go with either car. The MR2 isn't as common as the Miata is, but the Miata isn't THAT common to begin with.
Stock, The MR2 is a better performing car. Depending on the year you get, the Miata has slightly less or more power, but the MR2 is lighter. On the other hand, the Miata has a larger and better aftermarket, and likely more potential for power. Plenty of 200+ RWHP Miatas on Miata.net. Lets also not mention the possiblities for an Engine Swap if you want to get even more exotic.
There is also more documentation on the Miata, more books, and more resources (Miata.net is a HUGE resource) for information.
Reliablity is also a concern, I am not sure how the MR2 fares as far as reliability goes, but knowing its a Toyota, it should be top notch. I cannot comment on this, however, I will comment on the Miata.
Miata has the 1.8L thats been around forever. I currently have 108k~ miles on my car, and it still runs strong. I also feel that the Miata will be easier to work on than the mid-engine layout the MR2 has. I personally have never worked with a mid-engine car, but I don't hear many good things about them.
Also, Toyota is discontinuing the MR2, and I have a feeling that might drive up prices for parts if anything ever breaks. Not sure how it'll affect resale value as well (could be positive or negative). On the other hand, Mazda is changing from its 1.8L to a 2.0L(?) on the next generation Miata, that might affect part prices as well.
Regardless, of how I feel, I believe you'll have fun in either car. There are plenty of other roadsters I rather have than a Miata (S2000, Z4...), but I'm not quite sure about the MR-2. I guess I'll need to drive one.
I know this is likely pretty biased towards the Miata, and I don't blame anyone for looking at it this way. After all, I do drive one. But I do believe I am being fair with my accessment.
I'd drive both, see which one you like better, then go for that. I will tell you though, as a Miata driver, I've enjoyed it alot.