This sentence of the documentation is outdated. With a recent version of Eigen, LLT should be much faster than LDLT for quite large matrices because the LLT implementation leverage cache-friendly matrix-matrix operations, while the LDLT implementation involves pivoting and matrix-vector operations only. With the devel branch your example gives me:
LLT decomposition & solving in 380 + 4 ms.
LDLT decomposition & solving in 2746 + 4 ms.