OK, first off... let me clarify something. There's a difference in which queue you choose to go. There are practice (now called custom) games, normal games and ranked games. You can only enter ranked games solo at level 30 (level 20 if you are a full team). So someone who has played 10 games will not even be close to entering ranked. Some might find this off putting... well it is what it is. This way, you go through enough weekly rotations to test out a fair amount of heroes and decide which ones you will buy.
So whether a level 20 plays against a level 10 is pointless, because it can't be part of the competitive part of LoL. Now if you want a concrete answer... yes. The level 20 will have a slight advantage, but then you have to take into account the fact that there are 30 rune slits, each unlocked as you level and different tiered runes. the point being that you only really gain any benefit from runes (real compressibility and something that you can see in game properly) at level 25ish when you already have the majority of your rune slots. Everything before that is to get you used to changing rune pages and respeccing masteries depending on which hero you're playing.
Another thing you should realise is that normal mode, ie: non competitive, works on a blind pick system. You pick heroes that you want, and the other team can't see who you've picked. It's only once you've started Ranked Mode that the Draft system comes into play. Now I assume that anyone who enters ranked games is well prepared for them and if not... that's their problem. If they ain't prepared to deal with the fire, GTFO the kitchen.
Last thing... the game mechanics are totally different. There are no INT/AGI/STR heroes. Heroes are separated by their allegiances in the game world and by their abilities and base stat progression. I personally think there aren't any hard counters, it's mainly got to do with in game items and who is the better harraser/farmer. Though there are definitely heroes who fare better against others, it's really minor in comparison to what items you buy and how you play.
All that said... I prefer the buying heroes to start with as opposed to getting all of them immediately. It allowed me to try them all without getting confused or without people putting pressure on me to choose hero x because of this or that reason. It also forced me to try heroes I wouldn't have tried otherwise (I never played supports in DotA, whereas in LoL I main a support). Fact is... some people prefer one way (all heroes at once and a game you can "own") others such as myself prefer it this way. Think of it in terms of WoW. You don;t start off with a level 80 (or whatever the cap is) hero, you have to level him/her before you can become really good and part of the reason is so that you learn how to play that class. Since LoL wants as many people to enjoy the game as possible, it is the best way to do it imnsho.
My 2c.
EDIT: If anyone wants to give LoL a swizz, if for nothing else than to be able to berate it properly, do the right thing and sign up under my account...
Signup Here. It's the right thing to do! Uncle Sam is watching you.