I started off with LSi9 and LSi15 several years ago. The LSi9 were nice, but I never could get used to the bass section of the 15. Coming from high-end headphones and thus being accustomed to well-integrated and well-controlled bass, those 8" side firing woofers always gave me grief. They did have a decent midrange, and didn't grate on the top-end, which was nice.
Replaced the LSi15 with Tannoy Eyris DC3 and Tyler Acoustic Taylo monitors (w/ the Revelator tweeter). I liked both very much, but in retrospect the Tannoy was the more complete speaker. The DC3 should be considered a significant step up from LSi15. The Taylos too, with the caveat of bass rolloff. The Taylos had surprisingly phenomenal "air", imaging, and soundstage, but that bass rolls off real quick. The Tannoy were just excellent all-around musical speakers with a sweet midrange and superb coherence from the dual-concentric driver (there's also a non-DC Eyris 3, which is NOT what you want). The Eyris DC3 is now discontinued and could probably be picked up for a very nice price (~$1K) if they ever came up. Tannoy also has newer lines which are also excellent -- I can recommend just about any dual-concentric floor-standing model from their residential line. Being a compact floor-stander, the Eyris DC3 won't have subterranean bass either, but it handled most music quite well.
My next move -- based on the excellent experience with the Taylos -- was Linbrook Signature monitors, and...that was a mistake. More bass yes, but the magic from the smaller sibling was gone. Next move from that was Legacy Signature III, and while at times they showed some promise, I just never got into the groove with them for any *extended* stretch of time in my system.
