What the heck, I'll throw out a couple of suggestions, with the huge caveat that I am nowhere near the top owners on this site in terms of overall performance at higher caps. Everything below should include two other caveats: "in my opinion" and "there are exceptions to every rule."
1.) At lower caps, the fundamental principle of roster building, IMO, is value/$. Salary rapidly becomes scarce, you want players who can deliver good performance relative to their cost. Seems obvious. But the higher the cap, the less salary becomes your primary constraint - and therefore the numerator becomes more important than the denominator. Taken to the extreme, at $255M you basically stop caring about salary altogether.
2.) Four examples of value that are important at lower caps and less so at higher caps: speed, SB ability, switch hitting, and range. Note I said "less important" not "unimportant." An A+ range outfielder who can hit - like Speaker - is still more valuable than a D-range hitter who can hit at a comparable level. But someone like Max Carey (a staple in OLs and even at 100M) becomes much much less valuable at higher caps. All the plus plays in the world won't make up for the number of runs you are giving up at the plate compared to using a better hitter. The higher the cap, the more you will find that you need every player in your lineup to be able to hit at a hall-of-fame level. If they can't do that, then you are at a huge disadvantage at that position, no matter what other assets they bring to the table.
3.) The higher the cap, the smaller the number of players who can legitimately contribute. This is especially true of pitchers. There are literally thousands of pitchers you can reasonably use at 80M. There are far fewer at 140M. It's also common at 80M and lower caps to have 1-2 mopup pitchers, and another 1-2 Long B guys or spot starters who are really innings eaters, used to stave off fatigue or to soak up IP in a blowout. You are much less likely to see rosters with those kinds of pitchers at higher cap. You want every one of your pitchers to be studs.
4.) Fatigue becomes a bigger factor. At lower caps I am comfortable using anyone at fatigue levels down to 90, and in some cases below that. At higher caps, I don't want to give up any performance. Note that this includes in-game fatigue for pitchers, so I manage PC more aggressively at higher caps too.
5.) Bench quality is more important
Your mileage may vary on all of the above. Hope others will share as well.