Okay so I get that some champs are just better then others, so who will be more useful in Dominion?

I main heimerdinger and I am excited to see his defensive abilities in dominion. I feel like he is one of those characters that will work perfectly on this map.

I think nidalee will be good
she can hit people through walls with her spears to prevent capture.
she can lay down traps that provide vision
she can heal so she will be nice and sustained
her ult increases run speed speed, no mana cost so more sustainability. good farming also.

Durable champs with anti-attrition built in. These are the ones that may end up being considered OP.

It was mentioned that the addition of health shrines was designed to specifially counter their large advantage. It is likely this won't be sufficient. Especially since the durable champ can use it too.
So a list of such champs might look like, from MORE likely to only POSSIBLY:
Mundo
Garen
Blitzcrank (i'm biased, but I really think so)
Fiddlesticks
Gangplank
Irelia
Vlad
Mordekaiser
Warwick
Nunu
Nasus
Swain
Nidalee

I can't comment about stealth champs or healer supports, but i'm sure they'll have some kind of useful niche. Karma might become popular on this new map because her kit seems built for it (Harrass, sheilds, aoe heals, speed buff/debuff).
Heimer will obviously have a strong role as well.
I want to put some emphasis on how terribly OP Mundo is gonna be. While mundo is widely considered to be crappy at reasonable levels of play on SR, he is an absolute beast on TT because he is great in small fights and skirmishes. Cleaver is a low CD, Decent damage, long-range poke. His ultimate gives him bonus speed and puts him back in the game, it is also on a fairly low CD.
If you've played 3v3s you know what Mundo is gonna look like in Dominion.

Renekton will be great, is slash and dice+ruthless predator combo gives good movement and provides him a good ganking and counter ganking ability.

I'm afraid that champs who are based on farming creeps (Nasus+Veigar) will be at serious disavantage: beginning at Lvl 3 and the overall game setting gives them far less time to boost their Q before it matters

On the other hand, Tryn might be favored because this cuts his weak levels by half before he can get his ult.

Pantheon might also be good: I believe the map may give him a logistic advantage for his ult.

Garen looks like the best I've seen so far; I'm thinking Panth will be good too, maybe even Eve (dat lvl 3 burst on squishy)

Im not too sure Swain will do well in Dominion. For Swain to sustain extremely well in a map he needs to last hit EVERY mob for the mana. His ulti drains that mana quicker than he can get it. Sure he can harass like a boss but his 3 move combo takes about half of his mana at low levels. He will be rather debatable.

Champions controlled by players who actually know what they're doing will almost certainly perform better than champions controlled by drooling idiots.

Just a hunch.