I am with LSV, great policy/features and incredible price, but no I haven't had to claim.
Shannons on the other hand I will never deal with, EVER! I am sure they give a good service, but they treated me like a 13 year old school boy, and have lost a customer for life (one that has kept his car fully insured/registered even though it has spent the last year off the road, and probably the next 10) and hopefully every potential customer that will listen to me.
I said I had a 260z 2+2 that I wanted to insure for 15k and they just laughed at me (wouldn't even listen to what was actually done/modified to the car). The guy then went on to explain that he was a huge NISSAN fan and new everything about NISSANs and that because my car was a 2+2 that my car wasn't worth more then 4k (My computer cost more). He essentially called it a bastard son that no one wants, I think his actual words were "people generally only buy those for parts".
His justification was that his mate had just picked up a 260z 2 seater that needed a bit of work for 6k (At the time my car was a L28ET, with Motec M600, brakes, rust repaired, painted, wheels, etc, I.E. Better condition then it now sits). AH, it still infuriates me.
Not to mention after all that he said that if I was to opt for a 8k valuation (which he didn't think my car was worth) that it would cost me 2k a year.
So end of the day, I will take my chances with LSV over Shannons any day of the year. At least they were interested in what I was passionate about, wanted to know all the details/pictures I could give them and were willing to give me what ever price I wanted for my car.