There are two separate issues here...if a fault develops out in the system, then it's BT's responsibility to fix it. However, differences occur in how your initial complaint is dealt with...efficiency, politeness, interest, follow-up communication, compensation for lost connection - all the things that come under "customer service"....and this is where some ISPs excel and some fail miserably.
On the rare occasions I've had to report problems, I've been impressed with the John Lewis level of care...the staff are Plusnet's, working for JLP. Yes, Plusnet is owned by BT...but run completely independently (thank goodness!). And I don't mind paying a bit more for excellent service.