I had a 98 NB mx5 for a good number of years. It had a very different feel to an mr2. The simple answer is test drive both, as you will quickly figure out which one you prefer.
For me, the mx5 felt very easy to drive hard straight away. Feel like centre of gravity is lower and less weight shift overall. Very adjustable in the middle of a corner, lift accelerator slightly or dab brake is all fine in the mx5.
Part of that is also the lack of power, with less power you have the sensation of being able to thrash it safely.
I drove a couple of older mx5 NAs when I when I decided to get this mr2, and the lack of power turned me off them. Our 2008 Ford focus family car felt a lot faster ;p , couldn't see the point of getting a slower "sports" car.
I am comparing to a Turbo mr2 so it is a whole different league. It feels quick, it handles like a light sports car, but definitely more weight shift than the mx5. It takes longer to feel comfortable, but still handles nicely. I don't get the sensation of being able to drive it flat out on the road though like an mx5.
I think I would still prefer an NA mr2 over an NA mx5.
A big thing the mx5 is so much easier to work on, nice big engine bay with a small engine :p, bulletproof engine too but not very refined.
Looks wise is not even close :) mr2 looks way better. Mr2 interior much nicer too.
The convertible thing was never a big deal for me either, I had hardtop on the mx5 by choice.
A very tight winding road like Mt Buffalo in Vic, ill take an mx5. Everywhere else ill take the mr2.