I've now done 5 battle drafts and I can say they are a complete waste of time, as is. Maintaining a winning position is far too easy and coming back way too hard with a shared deck. All of the minor flaws of the game rules get magnified and made more frustrating. For example, territory grabs become almost permanent: just try taking back a flux well, it just isn't going to happen with you sharing buildings and creatures. And because you're sharing the same deck of the same race, natural different domain counters aren't an option.

Also, with cards being random and rares being weighted towards tier-3, the person in the lead will get more rares and the person behind will wind up with commons and a few uncommons. Overall, the prizes are great for the winner and absolutely terrible for the loser.

but that is how it should be right the winner should get better cards than the loser?

About the territory grab, you know what they can place so you should be able to prevent the grab in the first place. I think the strategy is just very different than the normal game.

As both players have same cards, the main advantage should be that player exactly knows what his opponent is able to play.. so this is sounds like much more logic to me, but of course I haven't tried it myself =P Not going to loose 225g with 50% chance (even though I know there is also 50% chance of winning 225g).
So.. skill is what counts here in my opinion. Worse is, that one mistake and you are probably out of game, unless your foe does one himself.. (and much bigger one.)
Counted; yes, I like the idea of Battle Drafts, would like to see some free ones as well, so I can ever play it

I would say that battle draft is far more luck based than skill based. If both players could play the same cards it would be skill but since only one player can play each card most games come down to who can play the best cards first. Since there are so many common cards in every domain that would never make it into a normal deck the power variation on cards is even higher than usual. There are also many cards that are become useless with a shared hand and domain. Most starting hands will have 2-3 domain buildings 2-3 useless cards and 2-3 playable cards. The number of domain and useless cards does not change much as the game progresses but the playable cards get used very quickly. Being able to get the only 1 domain creature is very strong. Out of 5 commons the odds of there being only 1, 1 domain creature is about 40% for all domains. And even if there are more than 1 whoever goes first will get the better one.
Also there are no "tricks" so your opponent will always know exactly what you are capable of playing and if they don't want you playing it they can play it first.
And unlike keep cards where the average prize + cost of cards is worth more than the entry fee in battle draft you get exactly what you paid for.

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I changed it yesterday so that more cards are drawn. So now a lot more cards are cycled through thus making it less likely that one guy will get all the good cards.

This is the main problem as I see it right now. I've won a few battle drafts which I didn't break even on (and that's with playing any rares that I can). I've also played a couple where you run out of playable cards pretty quickly. 55 between two people is 27.5 each, but considering that about 10-15 of those cards are going to be useless/unplayable you wind up with about 20-22.5 cards each which is less than a normal draft deck. I think adding in another 10-15 cards would solve both issues, but an increased hand size would also help. Jed's improvement of quicker card cycling does increase playability as well.

I also like the idea of each player picking a domain to draw from, but once the game starts domain is shared between players so you can always cast the same things. It would even it out a bit I think.

After playing about 15 or so battle drafts, I have to sadly confirm that the format doesn't make any sense to play, in terms of current payouts. If you lose, you're generally down quite a lot of value and even if you win, you have to get lucky to break even. You're on average better off just opening the packs yourself, even if you're a very good player.

It's a shame because the format is rather fun (when it's not incredibly frustrating).

Also, random domain is not all that fun: I've had 0 elemental, about 9 MF, 5 DL, and 1 sylvan. A mechanism so that the players choose their preferred domain and either one of the selected is chosen or a combination is chosen would seem to work much better for player satisfaction.