A complex question... first the simple bit, CI is not affected by seating - just marketing, aircraft age and staff morale/layoffs as far as I know.
As for seats affecting LF, it is complex. Better seats means fewer seats, so if you are in competition, you will lose pax allocation as you will be offering a lower portion of available seat kilometres - this counts for more than the marginal boost from increased comfort. If you are not in competition, you will also lose pax if the better seats mean you cannot supply route demand fully.
However, on longer flights pax do like better seats (they nominally want S for 2+ hours and P for 5+ hours, or so I've heard... not many airlines in AWS meet these demands at these points though!) Therefore, if seat type would make a difference because of the flight time, you are better off fully supplying a non-competative route with nice seats than lousy ones. It's only if you try sending pax on 5+ hours in HD seats that you'll really annoy them though!
So, all a bit of a mix-up really, and I'm sure others may feel or know slightly differently. To be honest, I only worry on long-haul about my seating really, more often than not if I offer nice seats it is to better fit an aircraft capacity to a route than to make pax happy - if I can make them happy I do though.