Keep passive gold/experience gain and mana regen. Axe the rest.

As everyone has said, Mana regen should stay; Without it, mages would take a huge drop. It does make AD casters like Pantheon a lot stronger; If there was going to be a class based aura, I think it only really works if you make the mana regen class based (So mages are higher than AD casters).

And on the topic of aura regen, a lot of manaless characters are weaker because mana characters get this boost. In SR, specifically ninjas and furys, are stronger in laning but weaker in team fights due to not having as many resources. Since Dominion is a team fighting game, making them even weaker hurts.

To go down specifically:

Ninjas: Shen, Lee Sin, and Akali range from good to okay; Kennen and Zed not so much. Energy regen in the aura would help a lot (Or a flat maximum energy boost)

Furys: Tryn and Renek are among the worst champions because of this. Shyvana is better but not great, and the reason Shyv is better is due to passive fury gain (And that it really only affects her ult). I think a passive fury gain should be TESTED but might be too strong (Especially on Shyv, might have to exclude her from that); Making it so that fury depletes at a LOT slower pace (or not at all) might be better (Again, this would have to exclude Shyv, otherwise her ult would stay up haha) but honestly might not be enough to have a big enough impact for Try and Rene.

TBH that's actually probably about it when it comes to manaless problems.

HP: Vlad/Morde/Mundo are okay at worst, and morde is a good bot
Heat: Rumble's good
No Resource: Garen/Riven/Kat are all pretty decent as is.
Ferocity: Cuz Rengar needs buffs.

What if the aura was changed to only affect bonus mana regen?

It really helps me know I can build more openly and use either flat pen or % pen for most of my damage dealing champions. For me however it feels useless as a tank. More damage is nice, but really on dominion you build them as a wall who can hold a point and let the tower or your allies kill enemies. Probably helps with bottom however.

The large general aura provides a huge, benefit to ability spamming, mana-using champions. It makes a number of different champions viable and able to repeatedly fight to take and then defend a point against attacks rather than going through a full fight and then having to back right away because of low mana, (i.e. has some mana left but not enough for an extended fight as tends to happen in the 1v1, 2v2, scenarios). I'm thinking of champions like: Talon, Warwick, Blitzcrank, Skarner, Jarvin, Jax, Pantheon, Sion, Trundle, Udyr, and Xin, just off the top of my head. In the early game a couple full rounds of their abilities and you are usally about out of mana with SR or TT mana regen. I fell like taking the mana regen away from these champs and giving it just to mages would really hold them back and drive them down to lower tiers.
Another thought, if you took away the generalized and gave specific buffs to specific champions or classes what would that do for some of the unusual but viable builds? Examples, Master Yi, do you give him the damage buff or the mana regen and magic pen buff? Same question with Sion and Shaco? Other even less common ones include, AP rengar, AD Kennen, Teemo (AP, AD, On-hit hybrid), Alistar (AP or AD), Malphite, Kayle, and I'm sure others that I'm not thinking of, what specific buff do you give them?
An idea, if you wanted to narrow the buff down what if you broke it down into various different buffs like, Armor pen, Magic pen, Attack speed, Mana regen, (maybe others) and let the player pick at the beginning which 2 buffs they want. This would allow the player to customize even further the style of play they want to have (kind of like Kha Zix who you can customize with both your build and your evolutions).

TLDR: Taking away mana-regen buff would hurt a lot of champions early game imo, only giving certain buff to certain classes would hinder fun off builds. I'm sure there are work arounds that could be done by riot (you guys do this for a living but that's my opinion.

I feel the Dominion Aura is a one size fits all approach to balance champions on the map, but we all well indeed know it’s very difficult to really have a one size fits all approach to balance. The only way the aura can be useful is if there is in tandem, a systematic solution to scale back the weird cases where a few champions become overpowered because of it.

What if every single champion had a different aura when on Dominion?
Pros: There’s more leeway to tune and balance each champion for dominion
Con: Expectations that champion A is the same everywhere is broken.
Is this really that bad of a con? What is best for the end user? Food items and retail chains retain their brands globally, but tailor to the needs of the locale, why not the same here? I buy a kit kat here in the US, while it’s different in Japan, I still recognize it as a kit kat. I still love kit kat, even though it’s different in different places.

What if you have a selection of auras to choose from – and select them similar to masteries/summoner spells? What if each champion only has access to a subset of these auras.
Pros: Allows the weaker archtypes to have access to what they need to excel in dominion, without the detriment to hybrids/alternate builds.
Cons: Slightly complex, may still make the stronger characters of an archtype imbalanced (if we’re still trying to create a relatively small and simple to understand set)

I'm of the opinion that the aura is *mostly* fine, although lowering the numbers slightly to compensate fot eh S3 changes or removing it could be worth experimenting with.

The mana regen part is fine.
Removing/lowering it doesn't really affect the stronger bruisers and such, but really hurts mages.

----

Also, I think having the aura increase either Energy regen or maximum Energy like someone else said would be a good idea.

Energy champs on SR are balanced (in theory) by having slightly weaker abilities with the catch that during the laning phase that they can use those abilities to harass to infinitely without being gated by running oom.

There is no laning phase in Dom, or at least not of a conventional type, which basically screws energy champs into not being able to fully spam their abilities during fights and gain nothing back.

-----

Also, can you perhaps make the aura decrease health costs on abilities?

Champs like Morde and especially Vlad basically hurt themselves with their own abilities, and the healing decrease aura lowers anything they might get back from it.

The mana regen, increased gold gain and free xp gain are important for Dominion to stay fast and fun. Removing any of them would slow the game down and make it less fun.

Personally I'd like to see a few things:

1) Mana Regen stays, but maybe lowered. Resourceless champs seem a little underpowered with how strong this aura is, especially with how less painful going back to base to charge up is vs. SR.

2) Penetration auras should I go. I never really liked them.

3) Healing Reduction should definitely go.

4) There should be a cooldown reduction aura. The games are so short that the cooldowns are just very painful. It'd be nice to raise the cap. It'd be VERY nice to have it affect summoners too.

Finally, and this is a little off-topic, but:

5) Per-Win IP Boosts should be the same as SR! I hate that I have to choose between wasting half the boost IP playing dominion, or finding time to fit an SR game in (I don't get to play that much). They are already a flat rate, so what's the point of cutting them in half for Dominion??