The LSA is rich and powerful and a solid presence. It separates with being clinical and presents without making a trademark on the sound. Nothing's really lacking with it at all. My only reason for thinking about a change is the feeling that separates will always be better than integrated. Whether that's the case or not I don't know.
The pre-amp section of the Statement is tube. I replaced the stock with Mullard 12AT7's for a richer sound. The Statement itself has duel-mono design within, with each speaker being powered by its own transformer, etc.
Tash also recommended the Antique Sound Lab Cadenza monoblocks for a real treat, but I would have to get a comparably quality pre-amp, and that's way out of my price range.