In competitive, would Pokémon I leveled up through just playing the game not have a chance? All my Pokémon have some of the best movesets and matching items for said moveset. But even then, would these 'average' Pokémon get trampled most of the time?

Sadly, the answer is yes for most competitive groups. I'm personally hoping it changes in X and Y because of how silly it is, not to mention how tedious it can be to breed for nice IVs.

I won't lie, careful EV training will give you an edge in battling over Pokémon that were casually trained. However, EV training does not guarantee victory for each battle- it only gives you a slight advantage.

Heck, I remember doing random PBR battles when Platinum just came out with my favorite Pokémon who were casually trained and they gave me victories against some teams that were clearly EV trained. It just all comes down to how you use your Pokémon, to put it simply.

In a major competitive environment, normally trained Pokémon would end up getting trampled. If you want a secure way to battle in a competitive environment, then you need to invest time into learning EVs and IVs.

As said above, EV training does give you a major edge. It allows whatever stat you choose to become super powered even though it has its limits. But that doesn't mean regular Pokémon aren't useful.

As long as you're not unlucky (with all low IVs and a bad nature) then your Pokémon could still have potential. My good ol' Darmanitan from my Black playthrough was able to take down an entire competitive team once (not alone, but it was major help.) It really depends on the skill of the player to make the competitive/non-competitive Pokémon work.

They DID say management over EVs and IVs is going to be easier in X and Y. I still don't know if that means we only SEE them or make breeding for IVs and training for EVs easier.

I remeber when i got into this ev training bis, when dimand and pearl first came out most of my pokemon from my emerald i brought over got destroyed by ev trained pokes. At the time i was just learning how to ev train. But like the others said it depends on your skill to use average trained pokes against ev trained ones.

Reuniclus and Turtwig have it right.

EV Training and IV Breeding will give you a noticable edge in competitive play. It will not guarantee victory, but the edge it gives definitely helps. And that edge over Pokemon that did not have this training/breeding is noticable.

Now, I'm not saying the pokemon you played through the game don't have a chance (I've wrecked things with one.) But it will most likely be an uphill battle.
You'd have your work cut out for you.

I dunno. If you got yourself a Rain team *not EV trained* going against a weatherless team that's EV trained, the odds of you winning are still up there, depending on how you play your cards and if they don't have Conkeldurr ( Bad experiences). Regardless, EV investment really gives you a good boost in competitive play.

EV training will give you a MAJOR advantage; this is coming from a person with no proper ev training charging headfirst into the 2010 Pokemon VGC's. If you intend on winning sometimes, then yeah, you should probably do that.