Big 4 Risk Advisory Offer vs Small Strat Firm (Advice wanted)

I am a senior Fin/Acct major at a top 50 state undergrad business school. We are Big 4 target but not MBB/IB so I know where I stand. I have a 3.7 and decent involvement. I currently have an offer for BIg 4 Enterprise Risk Advisory after I graduate which I got from an internship. I enjoyed the people and the work was also enjoyable when it wasn't tech audit focused. However I am a little more interested in strategy compared to audit/risk management. 

I want to weigh the advantages of a Big 4 name vs a small no name strat/research firm that I think I have a chance at. I want to set myself up for the best careers opportunities if I choose to leave either type of firm. 

Also I would really appreciate any advice on the importance of firm name vs specific strat role. Serious adivce and questions only please :)