Their performance are actualy very simalar. Yes, the miata has the edge which is shown in autocross results but the crx is right there behind it. The CRX is also easier to drive at its limits then the miata which can help keep you consistant.
Assuming both cars are taken care of well I would go for a CRX for a daily driver. Hardtop plus a good fair ammount of room to put stuff, CRX wins that hands down. for pure fun weekend warrior/autocross car I would have to give a slighter edge the miata, RWD, topless roadster fun.
On the other hand, finding a good well taken care of CRX that hasnt been boy racerd out can be hard these days, and they tend to go for a pretty penny. The vast majority of miata's on the other hand are treated simply as weekend cars and are usualy babied. So finding good clean miata at a fair price is not hard to do by any meens. I almost purchased a black 94 miata with hardtop and 70k miles on her for about $3000, unfortunately I wasnt able to get out there to take a look at the car in time before she got sold.
*also, look in to first gen CRX's, they are even lighter and dont sell for as much as the 2nd gens(becuase they arent mad jdm tyte y0 and dont have as many body kits avaliable for them...)
*edit: If this is for drag racing I wouldnt get either of the cars, LT1 camaro/firebird's, 5.0stang and turbo 2.3 mustangs, merkur xr4ti's, starions/conquests,mk3 turbo supra's, turbo DSM's, TII rx7's can get you quicker times for less coin/work. But if givin the choise between the two I could go for the miata simply becuase its RWD.
Swaps for the miata's, I have seen them all. from 5.0mustang engines to LT1's to LS1's, to turbo ford 2.3 to 13bt. Honestly I wouldnt bother with a v8 in a miata, thats althought sadisticly fun just overkill for such a small car with small tires. The chassis was not built to withstand the torque and I rarely say this but the weight of the v8 can change the chandling characteristics of the car(even the ls1), same goes for a turbo rotary engine.
"I" would personaly go with a later miata 1.8 engine and turbo that. That will give you more then enough power for such a little car with such a small wheel base.