Both large and small diaphragm mic’s are in common use for overheard drum mic’ing.
For many years I used two Shure SM81’s over my drum kit and if I had to make a recommendation for a pair of reasonable priced, well respected condensers (for this application) … I would say get two SM81’s but at about $350 each, I think you are already over budget.
I don’t have any personal experience recording with two overhead large diaphragm condensers but a model that will often come up in discussion is the AKG 414 (in its various forms). But now you are in the ballpark of 2 grand for a pair.
When comparing SDC and LDC mic’s, engineers with a lot more experience than me (I am not an engineer just a hobbyist) ... will talk about transient response and frequency response. A review for a SMC might discuss how well it captures cymbal detail (transient response) and a review of a LDC might discuss how nicely the toms and bass drum are presented.
Currently, and just to convolute matters even more, I am using a pair of Beyerdynamic M160 ribbon mics.