I think there's an important distinction to make here, in that you're really asking two (not directly related, from a credit score perspective) questions:
Should I close this account
From a purely credit-score perspective, no - definitely do not close this account. Carrying a credit card account you're not using usually has a net positive impact on your score:
- it helps keep your average utilization low
- it will slowly help your average age of credit go up
- it will help keep your credit mix good
You also asked,
and try to get another 0% offer from a different company?
I always clear the balance, but I like the comfort of being able to carry a balance, should I need to
If you're thinking about this from a credit score perspective, opening another account will have a number of impacts:
- the hard pull on your credit report (which the bank will do to approve your application) will drop your score by a small amount for a short time (a few years)
- your average age of credit will drop, because the new account inherently has a zero age at first. This will slowly creep back up as the new account gets older
- your average utilization may go up or down, depending on whether or not you actually do ever carry a balance.
Of course, if you do literally need to carry a balance, having the promo rate is a good thing. But if you never plan on carrying a balance, and you're concerned about your credit score in the short term, it probably makes sense to not open the other account. If you're concerned in the long term, it's probably a wash, since:
- two cards sitting at zero aren't any different than one sitting at zero from a utilization perspective,
- credit mix won't be substantially different
- average age of credit - in the long term - will tend to balance back out
- the hard pull will eventually age off.