Elias is exactly right - few more data points on this:
1. A classmate of mine spent 2 years at Infosys (tier-2), but started from ground 0 at Strategy& (bottom of tier 1 perhaps?); a year later, he still thought it was definitely worth it - and he is now about to make partner there!
2. While interviewing at BCG (as an industry hire), I was competing against a consultant from Strategy& who wanted to move up the chain; I got in, he didn't
3. My very first BCG partner was an ATK senior principal who came to BCG as a junior principal; years later, he was extremely happy with that move
4. While at BCG, one of my colleague had done 2 or 3 years at a boutique firm earlier, and he was outstanding at BCG, promoted early & all; now a principal
Bottom line: You can switch/move up, but it is no slam dunk and that might mean losing a couple of years of tenure; if you do manage the feat however, odds are you'll be really good and have a successful career in that second company if you are a cultural fit