Are there any significant speed up in time on cracking an RSA key (either brute-force or factoring with general number field sieve) using a GPA or FPGA compared to a CPU? If there is a speed advantage, are there any figures on how much it is?
FPGAs are not like CPUs or GPUs, and cannot be compared like that. Your question lacks sufficient details to provide a meaningful answer. FPGAs come in wildly different sizes and offers paralellism only limited by the logic resources of the FPGA. A giant €100000 FPGA will have way way more logic resources than a €1 FPGA. There are no €100000 GPUs or CPUs.
You must include other metrics to make a meaningful performance comparison. Like investment cost, power usage, implementation effort, and so on.
If you want a hint of high end FPGA capability: Some of largest FPGAs available can do up to 5-10 trillion multiplications per second.
Idk why people were so harsh, when obviously "a" would still mean comparable market positions (whether you meant "the best one money can buy", the most sold in the consumer market, or just whatever 1000$ could bring you home).
GPUs or even FPGAs the problem is still the same at the end of the day (until some new progress in integer factorization theory is made at least): you want to use sieves, not "as simple as it is linear" brutish algorithms. And for an big enough key that would really make you feel constrained by a normal processor, the downside to that is that they take an increasingly large quantity of memory. Which in turn comes in "ample scalable sizes" only for CPUs.
When factoring 1024-bit will enter the realm of sub-million dollars hardware, perhaps you may even see dedicated circuitries (ie. the premium you pay to design a whole new thing is worth the gains you get, and you won't throw away the device after just a few runs because you are only gonna be able to crack like 3 keys each two hardware refresh cycles). But without big juicy fruits in the near future, you can see why that's not really a thing.
Anyhow, for the moment, I think the best speedup is coupling GPUs with CPUs.