Going to an internship interview while already having another internship offer?

Hi guys,

I recently received an internship offer from AAA company (this is PE, not super big tho)and I already said thank you to them, although I did not sign anything on paper yet.

Meanwhile BBB (one of BBs but not GS or MS) company also wants to interview me for their IBD internship position.

When BBB interviews me, there is 100% chance they will ask if I am interviewing with other firms. Should I tell the fact that I already have an offer from AAA? Then, BBB would ask, why am I even interviewing with them. I would have nothing much to say, since I think either way makes me look bad. 1) ditching AAA also shows to BBB that I am not trustful. 2) taking offer from AAA means I just wasted the interviewer's time.

I know there is no guarantee that BBB will also give me an offer, but I feel I need to have a straight plan before I walk into an interview with BBB.

Brand name wise, I guess BBB is better because it is BB.
In terms of learning opportunity, I really cant tell. I think PE experience is unique itself, especially because I want to get into PE some point later in my life, I think having it now can help me later on to leverage on it to break into full time PE. (no?)

On the other hand, BBB is a sell-side BB firm, and I think sell-side keeps intern much busier, and therefore you learn more and pickup more skills. Also, before breaking into PE like 5-10 yrs in the future, I would have to break into fulltime IBD first, and having internship from BB IBD and knowing the bankers can be more helpful than PE experience.

Both positions are off-cycle internships so neither of them lead to full time position.

I really don't know which move would be the smartest one. 1) go to interview with BBB, tell them first that I already got an offer from AAA and already said yes. Tell them that it is difficult for me to ditch away now, because the industry is so small and I cant destroy my credibility and burn bridge. However, tell them that IBD is where I ultimately want to break into and that I am interested in their next off-cycle position. (heard from someone I know that this position ends this dec. and they will hire new one next jan. AAA ends by end of dec. so it is a perfect timing. fyi Im taking an year off)

2) go to BBB interview, hide that I already have an offer, and take the offer if BBB gives it. I am not ditching AAA since I have not signed anything yet on paper. ( already said thank you and sent a thank you letter to AAA tho)

3) Don't piss off BBB by wasting the interviewer's time, call BBB and tell them the situation and reject the interview invitation.

4) other wise moves?

pls contribute your thoughts. thank you