It's not a fair comparison.
The 1275 is 50 year-old technology, and it's a fair amount smaller than even the smaller-displacement Japanese engines. And by "performance", do you mean drag racing, pure HP or something else? Also, the car and engine are two different parts of the equation.
Well anyway;
A really, really healthy 1275 *might* make 120 HP (in a SCCA Runoffs car). These engine have primitive knock-inducing combustion chambers and 3 main cranks. Forget about using street gas...plan on buying your fuel in 55 gallon barrels from a specialty supplier and you'd be renewing rod bearing every 10,000 miles (if you're lucky). A more agreeable state-of-tune might be about 85 HP. You could run street gas and have reasonable longevity. But this amount of HP would never beat a stock Civic (the good ones are about 150 HP) even if a Spridget *is* a fair amount lighter.
But a Sprite is tons more fun to drive and, like all slower cars, you have to really *drive* it to get the best out of it. A more-powerful car (such as an RSX, a CRX, an RX-7, etc.) will allow you to go faster without trying so hard....less rewarding, as I see it. For club racers, a Sprite is fun to drive at 10:10ths. A racing RX-7 could be downright terrifying at that level, for most of us (me, for sure).
I saw the Grassroots comparo between the Miata and the Midget. It was on a slow, autocross course, which plays to the narrowness of the Midget (and the Miata was still faster). I own a Miata and a Midget.....a stock Midget couldn't even come close to a stock Miata as far as sporting steet use or on faster autocross courses (and certainly not on a race track).
As far as modified race-cars, here's my observation:
A fairly ordinary Spec Miata (they have essentially stock engines) can make it around Summit Point fully 3 to 4 seconds faster than a hot 1275 Sprite (I just looked at our Nov 03 race-results and compared three SM Miatas with three 1275 Sprites). 3 to 4 seconds is huge. I did feel I could stay with the SMs in tight turns at Summit, but nowhere else.
Even the special head mentioned above by Alec wouldn't bring you to the power levels needed to go head-to-head with a fairly ordinary Japanese 4-cylinder engine.
I will tell you that Spridgets are *way* more fun to drive than Miatas, but that's a difficult thing to quantify.
Can't you tell by the smile on my face in the picture below? (Note: the Honda following me has been racing with same used, "junkyard" engine for the last 6 years, with no major work....they're fast *and* reliable).