Really a matter of taste, and of course budget since the LSi7s cost almost 3 times more if memory serves.
The LSi7s I heard at Tweeter were very pleasant at low and moderately loud volume, nice warmish sound, though a bit tunnelled and not great imaging. When pushed to high volumes (85db and up) I found that their lower midrange collapsed, Diana Krall's voice suddenly sounded muffled and just totally unnatural.
The Ascends are much more detailed and image very well, though the larger 340s do have a wider soundstage than the 170s. The 170s in particular have weak bass and I would not use them without a subwoofer. Their sonic character is not "warm" but "neutral"---very accurate, amazingly flat frequency response. And they can be cranked very, very loudly without distorting unlike many speakers costing much more.
For the price of a pair of LSi7s though I'd buy a pair of the 170s, a pair of the Alegria Audio Lings, and a speaker selector switch...I'd still save $200-300 and I would be able to use the Lings for certain types of music (simpler compositions with slower tempo) at moderate volumes and the Ascends for HT and complex/fast music at higher volumes.
Of course with the new SE Ascends coming out in mid-January, these might be even better. But they'll ever be "warm" like the Lings and LSi.
I was just curious. I have some 7s that I bought long ago while there was a major Fry's sale and I'm just now giving checking them out. Right now it sounds like the woof is really really really stiff. I'm getting barely any output there. The high's however REALLY sing. I really hope the mids break in as I do like their look. If they dont and I manage to sell these guys I may be looking to jump into the search yet again.
Right now an Audire Crescendo that puts out 75x2 @ 8. Not sure its 4ohm rating. Next week I'm buying a used old Odyssey Stratus amplifier so I'm hoping that the 150x2 @ 8ohms (again not sure what the 4ohm rating would be) helps give it a little more depth.
As far as the Crescendo's ability, it ran my broken in 9s quite well from what I remember. Maybe the 7s just benefit more from the extra juice, or they really ARE just in need of a good break in period.