One is a standard the other a library. BLAS covers a subset of what Eigen does, and Eigen can use BLAS/LAPACK routines directly from other libraries (e.g. MKL) for those things.
Eigen calls BLAS when appropriate and with no overhead and the code looks close to the math. Eigen also supports small fixed size matrices where BLAS is not appropriate.
I believe (haven't looked at benchmarks lately) Eigen has trouble beating a good BLAS implementation like MKL or BLIS at doing BLAS stuff, but it is more expressive and has the ability to do lazy evaluation/fuse operations. Anyway since you can get it to call your favorite BLAS/LAPACK library, these are really complementary projects.
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