Should I take an offer from a small fund?

I work at a tier-2 management consultancy in the private equity team, mostly focussed on CDD and post-deal strategy engagements. I've been offered an associate role at a small growth cap fund in London - should I take it, or hold my nerve and continue to try for one of the bigger names?

I've been trying to break into PE for c. 1 year now, hoping for one of the MM growth or buyout funds (think Inflexion/Pollen Street/Gresham/BGF). I've got through to two case studies at these types of funds, but always lost out to candidates from IB and MBB consultants.

This offer isn't exactly what I'm looking for (much smaller fund and not in sectors where my experience is) but I'm acutely aware of the difficulties of moving to the buyside from T-2 consulting, so should I just take it and use leverage it to get something better in 1-2 years time? Or would it be better to keep getting deal experience under my belt and go hard on recruiting again in the future - considering I'm already 3 years in?