My understanding is that both are software performance tests. What are the differences or nuances in usage between the two?
性能試験 is simply performance test, and is used widely in many fields related to engineering, including software engineering.
I don't think 強化試験 is a common term, but judging from usages found on the net, it seems to refer to additional tests to ensure something (performance, conformance, stability, etc) You may need to ask your colleagues what 強化試験 actually refers to in your company.
Like you mentioned, 性能試験 is a performance test. If it's a server side, checking how many connections can be handled or how long it takes to return a response. Mainly focusing to know its performance. But the case of 強化試験, It's for finding bugs. And it's not a regular test like unit tests nor integration tests. It simply means a additional test for finding bugs. in another way to say, it is a test of 強化(quality enhancement)