Super caps are relatively new technology compared to regular caps and so each manufacturers models tend to be very different in many ways from those of other manufacturers. There are several makers who specifically recommend their supercaps for high discharge rates. I believe the AVX lineup (
https://www.electro-tech-online.com/custompdfs/2007/10/bestcap-1.pdf ) of supercaps should work well in this kind of application. There are many others out there, and it is best to study their datasheets to answer your question. The ESR spec is critical, and usually the supplier will specifically address whether their supercap is suitable to high discharge rates or not, usually in the applications notes section of the data sheet.
My experience is that supercaps do indeed work more like capacitors than they do like batteries. In other words, there is no memory effects, you can charge them up about as fast as you can discharge them, and they suffer few internal losses. However, they start behaving differently depending on how fast you are trying to push current in and out of them, in other words do not assume they work like most capacitors as the frequency of current in the application goes up. I have not tried them in any high frequency applications.