To me it appeared that the gear that drops from the new heroics is mostly build around avoidance.
I went avoidance because the gut feeling that there was more on the gear.
As I'm slowly gathering the T13 equipment, I see a steady incline in mastery. So, I guess I will be switching back soon.
Maybe somebody can shoot on this assumption with raw numbers.
As for what is better, think the situation will change that every time.
I read that tanking groups (as happens a lot in the heroics) would work better with an avoidance build.
Summary: both will work, see what your gear gives you, decide on that.
Pretty sure reforge calculators factored in buffs and could guide you to a balanced rating. It's just impossible to do so if you are avoidance spec'd. At least Mr Robot does.
Though the difference in avoidance is usually less than 1% unless you are really horribly unbalanced in ratings.
Most tools will properly balance dodge/parry. AskMrRobot does (but will change your gems too) and WowReforge does an amazing job of it.
If anything it's easier to balance dodge and parry if you're stacking avoidance, as you get to pick your gems sometimes. Unless you're just unlucky enough to have a ton of parry on your gear, or something.
At the start of 4.3 I redid all of my Firelands gear for Avoidance, and had only a 45% chance for a hit to land... And was balanced almost perfectly.
I've since gone back to Mastery (nearly 4500 rating now. 210% of my DS's heal as a shield ) at the behest of my healers. But I have been having to balance my dodge and parry ratings manually since getting Resolve of Undying and it's stacking 880 dodge. As no calculator I am aware of includes the proc in my dodge rating.
Everybody thinks Mastery got a huge buff because Death Strike no longer misses, but the Bone Shield change can be seen as a buff to Avoidance also. It's possible on some fights to maintain nearly 100% Bone Shield uptime if you can avoid enough.
As for Avoidance vs. Mastery. As many of said here; you may do either. But if your gear is obviously favoring one or the other (and no amount of reforging can counter balance it) you're better off rocking what your gear says you should.
The more you Avoid the less damage you take, and the less your Blood Shield is. And the more Avoidance you have, the better it gets. So pick one and stick to it if at all possible. That's all that really matters.
Avoidance is supposedly better on multiple Targets, or for if you want to Heart Strike more. -- It's also better if you're not one to optimize your rotation for the maximum number of Death Strikes
But, in my opinion, if your healers are any good at all, ask them.