During evolution, the character's base HP/ATK/DEF drop. Any ampies, skill level, affection %, equipment slots remain unchanged, except affection boost is doubled after evolution. Passive skills also improve after evolution - for instance, Saffron Tulip's ability of increasing defense by 3% for 2 squad members is something you'd forget about, but after evolution it will give said squad members a damage reflection.
Basically, if you've maxed out affection for the character, evolve them. Otherwise, you might as well leave them at max level for a while.