Sell side

Buyers often require acquisition financing, which only the BBs and large integrated banks can handle (e.g. a bank needs S&T and syndication capabilities). In addition to providing financing (which carries a higher fee than M&A advisory), the financing banks will often get M&A advisory credit. For example, financial sponsors (PE firms) looking to buy a company will often use BBs purely for the financing, but these banks get M&A advisory credit anyways, even though the PE firm might not even need advice. Thus, a lot of boutiques and MMs which don't have capital markets capabilities can't compete for certain buyside mandates (or at least can't be sole advisor) and will focus on sellside M&A.

Sell side deals usually carry a higher M&A advisory fee % for banks versus the buyside. Plus the client+advisors are trying to maximize the selling price = higher fee; in a buyside, the client wants to pay the lowest price possible = lower fee

On average, there is a higher probability of getting paid/closing the transaction in a sell side. In a buyside, a bank might be advising one of many interested parties.