I've recently become kind of interested in trying to get my pokemon as "powerful" as possible after learning about EVs and stuff (although I have to say that I'm still a noob at it). Anyways, a question that I've always wondered like my entire childhood is if it's best to evolve a pokemon as soon as possible. Like for example, lets say that my Abra just reached level 16 and evolved into a Kadabra. Should I trade it to a friend right away and back in order to get a level 16 Alakazam, or should I wait until it's level 30 or something?
For the most part, the stats are better than the waiting longer for moves. There are exceptions, such as Joltik in BW learning Bug Buzz a good ~14 levels earlier than his evolution and having no good bug moves until then.
In your case, most Trade Evolution Pokémon actually learn moves at the same levels as their un-evolved counterparts. And they stats are much more important than the slower leveling up- I'd rather have a Lv 20 Alakazam than a Lv 25 Kadabra.
You should look at the movesets. If it's an item evolution, you should wait until you have the level-up moves you want, because after evolving they'll probably only learn like 1 or 2 more moves via level-up. If it's any other way, then you should compare what levels they learn their moves at. I kept my Nidoran-F unevolved for so long in my HG Nuzlocke because I wanted it to learn Poison Fang. For most of the game, I needed something to hit Grass-types really badly, so it really saved me later on.
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Nope. A Pokemon's stats will catch up once it evolves no matter how long you hold it off.
Yeah, there are no negative consequences, but ingame it's probably more useful to have a stronger Pokémon faster. With a gym battle coming up and having an underleveled team, I'd want my Alakazam faster so that I can actually stand a chance.