What would you classify as the top MM shops?

Well you call yourself MM so LPs can sell you to their ICs as "alpha generators" and "complementary exposure" to the Apax-types.

I would call them large buyout vs mega buyout. Doesn't really matter. Call yourself whatever you want, the strategy is largely the same. Participate in auctions, pay way too much, do some add-on acquisitions to increase scale and average down your entry multiple, and then sell to one of your competitors so they can do the same thing. Clearly I'm generalizing here but directionally it's accurate.

Contrast with a true MM approach, where proprietary deals still exist (albeit not nearly as many as in the past). Main value-add is professionalizing an under managed and under-capitalized business. This typically means building out/replacing management team, implementing a metrics-driven approach and accountability, investing in organic growth (new products, increased sales and marketing, geographic expansion, etc) and typically add-ons as well. You come out with a far better business that will get you some nice multiple expansion on the exit.

When you have $3 or $4 or $5+ billion to deploy, you can't focus on these types of businesses. You need to deploy hundreds of millions per platform or the math just doesn't work.