FFT is great. In this instance it might even be REQUIRED because the MSGEQ7 is only 7 bands, while you can go nuts with FFT.
The biggest issue I found is that 8bit FFT is just not quite enough for some of the applications where I've ended up using the MSGEQ7. You can throw a 12bit ADC on it and get genuinely great results. Add in that the MSGEQ7 can sample at 160kHz+, and it's good for giving minute detail, though obviously, if you're going to use an external ADC, your bottleneck would be in the comms.
Anyhoo- regardless of which ends up being best, and why NOT try FFT first and see if it gives the desired result, this post is increasingly interesting to me.