Depends a bit on what you want.
CTC is very advocacy geared – lots of campaigns for better cycling infrastructure, their much publicised SMIDSY one etc. It all stemmed from their original aim of being geared towards the touring/recreational cyclist, they’ve become a bit more PR savvy and do some good work in upping the profile of cycling in general.
BC stemmed from road racing although they now look after most aspects of cycle sport including MTB racing. Yes it’s geared towards racing and your membership fee goes to supporting grass-roots/youth racing right the way up to Olympic athletes – if you ever fancy doing any racing (especially road/track) you’ll eventually end up with a BC Membership and racing licence anyway.
Both offer very good insurance should you be unfortunate enough to be involved in an accident, both offer discounts with various partners – BC members have a portal through to Wiggle which gives an extra 10% off everything for example.
You also get the usual email newsletters etc from both groups.
Pays your money, takes your choice etc.