So as far as what we know I think it's that:
Super Smash Bros. Brawl explicitly cut 2 characters: Young Link, who was being replaced with Toon Link, and Pichu, who might have been replaced with Plusle and Minun. After that they were planning on adding Roy, Dr. Mario, and Mewtwo, but they weren't high enough of a priority and time grew short. Strangely, Jigglypuf was going to be cut, but was added in at the last possible moment.
Super Smash Bros. for Nintendo 3Ds/Wii U is less documented, but we do know that the Ice Climbers would have been in if it weren't for hardware limitations, and it's implied that Pokémon Trainer, and thus, Squirtle and Ivysaur would have made the cut as well, though if/how the roster would have been restructured to accommodate them is unknown. We don't know anything about the absence of Lucas, Wolf, Roy, or Pichu, with the only reasonable guess being "priorities". The only one we do know wasn't given the green light from the get go is Snake, since Konami was never approached about it. Lucas and Roy would later be DLC.
That in mind, my guess is that generally, they want to keep as many characters as possible. Failing that, derivative characters seem to be on the chopping block first, as the non-clone cuts are Mewtwo (who they were trying to add), Squirtle, Ivysaur, and the Ice Climbers (who they couldn't add), and Snake. Even then though, Young Link and potentially Pichu are special cases, Roy and Dr. Mario made the planned roster for their would be second appearances, and Wolf and Lucas have no data.
So really, it seems like I've once again used a lot of words to say "I don't know nuthin'." Especially when there's likely going to be enough required cuts that they'd have to plan more cuts than they ever have, which is going to change their behaviour, at least a little.