What kind of speedup would I expect when changing -march from x86-64 (SSE2) to corei7-avx (SSE4.2/AVX)? I understand that my mileage may vary, but I see no speedup whatsoever, which surprised me. (-O3 in both cases.)

The current version of Eigen doesn't take advantage of AVX instructions yet, which is why you don't see any speedup when you instruct the compiler to target a recent architecture.
This is about to change though. There is a pending pull request to add support for both FMA and AVX instructions to Eigen.

Apologise for resurrecting this old thread. I see the pull request has been merged. Should I assume Eigen now has full support for AVX? Are there any benchmarks available?

Thanks

Matrix products for float and double on Haswell (AVX+FMA):
http://download.tuxfamily.org/eigen/gem ... aswell.pdf
http://download.tuxfamily.org/eigen/gem ... aswell.pdf