Nope. McKinsey, Bain, and BCG are the tier 1 everywhere. McKinsey is by far the biggest and best-known, but it's like MIT and Caltech. One is bigger, and one is smaller. The smaller is less well-known, but it's no worse.

In this case, the smaller companies are, if anything, slightly higher-end (more boutique).

I'm not actually sure the Tier 2 are trying to become Tier 1. It's like comparing Walmart to Tiffany & Co. They're very different business models, but upscale doesn't necessarily beat mass market.