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Listen OP, when a pokemon battles a lot, it gets stronger than a pokemon who hasn't really battled much, regardless of level.
However, it's not hard to "catch up" (since there's a limit for this difference), and it hardly matters during your first gameplay, it's practically unnoticeable. For more information on the subject, google "effort values", which wild pokemon do not have risen, but trained pokemon would get from your long journey.
traded pokemon ARE NOT WEAKER than your own pokemon, the exp. part is true, the weak part is not, maybe you got confused with something else.
You're gonna hear a lot of shit about X and Y (and probably ORAS), but truth be told, is a smooth, stable, good first experience for the franchise, the game was made for people who long abandoned the pokewagon, so, It's great you picked it up.
Just remember to have fun and catch a lot of pokemon, if you are ever interested in training better pokemon, simply start by knowing about natures, THEN figure out EV training, and THEN, and this is optional, research about pokemon IV (but this is the last more complicated stat, which matters the least)
