I've not done HC proper - I did the variant, using Mikl's nice Contented Cows link up. That said, we watched a party on the severely overhung first pitch of HC - which many say is more like a 24 to start your day. Definitely didn't look appealing for a 9 pitch climb (didn't do the last pitch due to the easy walk off option)
BBB is definitley not as demanding mentally or physically. The undies traverse alone is technically more than anything on BBB - followed by about 15m of vertical to the anchor.. and then a very technical 20.
I'd recommend you train a lot - go do some laps on some 3 pitch 20s. If you aren't over pumped; then you should be ready. See recent thread about your bail options from pierces pass!