Advice - 2nd year analyst in a sector-focused boutique

So a little background, I'm currently a 2nd year analyst in a sector-focused boutique. Think Allen & Co, code, qatalyst but more mid-market focused, though we have done a few $bn+ deals in the past and most of the deals we do now are $100m+. It's a very very good shop in its sector but it's not quite an elite boutique. I interned at a top 3 BB before my current role and I always wanted to return. I've been looking at roles for a couple of months now and landed a 3rd year role at a BB (think UBS, Barcap, CS, DB)

I called my operating partner on Friday to resign and he asked me to hold tight over the weekend so we could agree next steps. I had a 1.5 hour meeting with 3 of the most senior partners having a frank discussion over why I wanted to leave and whether I was making the right choice in joining a "lower-tier" BB as they implied. The thing is, I've been the star analyst there for a long time and they've given indications even before I resigned that they were going to fast track me to associate. During this meeting, they came up with a counter-offer, which I expected, but this one was a curveball. Headline terms: Bump up to Associate 2 (skipping 2 years, more responsibility, working direct with partners, etc.) + six figure "promotion bonus" (doesn't affect my regular bonus which is going to be fat anyway). This is something they've never done in their history, they don't bother with even a penny for a regular associate promotion

I've never wanted to stay in banking for the long term, I'm fully focused on buyside (having also interned at a mid-market PE) and my thought in making the BB move was that I was finally getting a platform. I've been heavily focused on execution (3+ live deals for the firm at any given point in time) over the last 2 years so I know I have to trade that in to an extent and I was willing to do so. My question is, will staying really limit my buyside exit opps given where I could go? Would decent funds (and I'm not interested in KKR, Bain, BS) look past the fact that I'm not a BB guy but at the deal experience?

Appreciate any advice on this