The advantage of stopping an evolution is that Pokemon can learn moves at a lower level than when evolved. After evolving, Pokemon will often learn the same move at a higher level, or in some cases, they will lose the potential to learn the move at all.
Is it better to stop Pokémon evolving?
The only reason you would want to stop your Pokémon from evolving is if it learns a move that its evolution doesn't learn (for example, Growlithe learns Flare Blitz but Arcanine doesn't, so you may not want to use a Fire Stone on it right when you acquire one).
What happens if I stop Pokémon evolution?
1 Answer. If you cancel an evolution for a pokemon that evolves when it levels up (I don't know if you can do it otherwise) then if it gains another level it will try to evolve again, so you don't need to capture another one just to get the evolved form.