Small Boutique M&A/TAS vs BIG 4 Auditing

Hi There, Just about me: My goal would be to ultimately settle in PE even though I could also imagine settling for M&A. Studied at semi-target school but had good GPA. Have internship experiences in a Fortune100 corporate financial role and a PE FoF.

As I am not sure if I can get a shot at the M&A department of a larger shop I was thinking about applying to M&A/transaction services of boutiques and the BIG 4. Now I am not sure if I should even apply to small boutique M&A shops as I am afraid that the lack of reputation of these jobs might make it difficult to transition to larger shops later on. In case I would not even get a BIG 4 M&A/transaction service offer, would you consider it a better experience to work in a tiny boutique's M&A team or BIG 4 auditing? Would it be easier to transition to Big4 M&A/TS from their auditing departments or coming from a M&A role at a Top10 accounting firm (e.g. GrantThornton, BDO)?