I'd hate to have to remember the rules and intricacies for each champion... multiplied by each map, by each mode. So yeah.. please don't change the rules and skills of champions! Keep it to the items!
They probably could alter base stats on a per map basis without running into to much trouble. That allows a bit of fine tuning on power levels but without changing the mechanics of how a champion plays. Even base ability damage and scaling could be nudged without creating confusion since it will only bump the output slightly without changing how or why an ability is used.
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Changing the champs based on the map would be a lot of work, and the wrong changes will trigger a MASSIVE qq fest from LoL community (cuz thats wut they best at).
Different item set is probably the safest bet on balancing between maps, not to mention it would be really cool for riot to be making more items.
And stop talking about TF2, thats not even a moba, each game has different situations and needs a different approach.