GStreamer is a fantastic framework for building complex multimedia pipelines, however what Spek really needs is a simple decoder and FFmpeg's libavformat and libavcodec do just that.
To handle some audio formats (e.g. APE and DTS), GStreamer relies on FFmpeg anyway, so the switch will result in fewer dependencies. It doesn't matter too much on GNU/Linux, but this will reduce the size of the Windows and Mac OS X installers.
Spek used GStreamer's spectrum plugin to perform the actual spectral analysis, with FFmpeg I had to implement it myself. The code I ended up with is very compact and gives room for a lot of experimentation, from using different window functions (it's still Hamming) and working on performance optimisations to switching to a faster FFT library.
The last bit is actually done, Spek now uses FFTW which in my tests is 1.5x to 2x faster than Kiss FFT used by GStreamer. Apart from that, FFTW can scale to multiple threads with near linear performance increase, future versions of Spek will take advantage of this.
UPDATE: As one of commenters pointed out, FFTs on small number of samples are not very parallelisable and my benchmarks confirm this. Also, I switched from FFTW to avfft which is built into FFmpeg. It's a little bit faster than FFTW for my particular use case. Lastly, 1.5x to 2x speed up was actually caused by a faster decoder, not by a faster FFT library.
Another thing that would be hard with GStreamer is static cross-compilation using mingw-cross-env to produce a single Windows executable. Because FFmpeg doesn't employ a plugin architecture, static linking is not an issue.
Last, but not least, the whole experience was very educational. I now remember why I loved C back in the days, the trick is to not even attempt to write any GObject code with it, that's what Vala is for. Fast Fourier Transform and the maths behind it is much fun, and NR was very helpful here.
For the curious, the code is merged to git master and pushed to Gitorious. The next version of Spek will be released sometime in July.