I run a Datsun 1200 at vintage races and instruct at PCA track days, I also instruct as do some friends who run Spec Miata, we all instruct and run the intermediate group as that is where we are lap time wise. My car with the 1171cc engine was belting out 80 hp at the wheels, the big bore 1508cc is belting out around 100 at the wheels (car is 183 with me in it). You do not need a 250-300hp car, you might need to switch run groups as yes in the fastest group the lap times are much faster.
For example at the last track day out of about 20 cars I was around 5 or 6th fastest in the intermediate group. I passed a couple of WRX STI's, Audi RS4, M3, Porsche 911s etc. In fairness the drivers are not as skilled or experienced. Part of the problem is they've never spent time in a lower power car (nothing really wrong with that, who doesn't want a nice car) and as such they don't really understand momentum. You do get the classic, stand it on the brakes, over slow the entry, no clue about rotating the car etc but it is a track day so in general they wave you past. There is also the (twisted, petty, small) satisfaction of catching and passing cars that should leave you behind. When I road raced bikes I ran little 125cc GP bikes and I always enjoyed guys on GSXR 750s and the like trying to figure out how you were 3-4 seconds a lap faster at a place like Willow Springs.
From an instructor standpoint a gutless car is a great tool; I've taken several students for rides in my 1200 and a friends Spec Miata, the usual comments are "wow, I had no idea that you could do that with a car" or my favorite of all time "man I have so much to learn, I need leave my car stock and learn to drive it".
While I like things with big power I find I enjoy pedal cars more because of the old adage driving a slow car fast. It also reminds me of riding little GP bikes, you need to be a complete animal skating it through the corners and really think several corners ahead.
As for Vintage cars I think they are more fun as well, at the last PCA day a Cayman drive made a comment about my 4 wheel drifting the car through a 90 mph kink. He said that his thought was that guys got a big pair, I brush it off with the I used race bikes comment but my first thought is doesn't everyone drive that way??
Sorry to be so verbose but if you want to run a vintage car or Miata or MR2 there is no reason not to, just run it in a group with similar lap times. Again it's a track day and we are not racing anyone, even I dial it back just a little for track days.
Tom