I looked up specifically examples of this and didn't find answers, they're buried in general discussions about why compiling may be better than pre-built. The reasons I found were control of flags and features, and optimizations for specific chips (like Intel AVX or ARM Neon), but to what degree do those apply today?

The only software I can tell benefits greatly from building from source, is ffmpeg since there are many non-free encoders decoders and upscalers that can be bundled, and performance varies a lot between devices due to which of them is supported by the CPU or GPU. For instance, Nvidia hardware encoders typically produce higher quality video for similar file sizes than ones from Intel AMD or Apple. Software encoders like x265 has optimizations for AVX and NEON (SIMD extensions for CPUs).