I kinda skipped cata, when I came back after MOP launched I leveled my war up first so I guess Ill give this a stab since I have both.
In pvp their in similar spots, with warriors being a bit better off this past patch 5.1 due to their blow people up macro and being able to sit in D-stance permanently in pvp. In 5.2 they're seeing a bit of a pvp nerf, and a few mechanical changes with OP, nerfed D-stance and shockwave/warbringer, and a few damage buff's especially to slam.
People have their opinions but pvp was much easier on my warrior, even when under geared. More controlled burst, better toolkit overall and far better mobility. I don't want to say it's faceroll, but even compared to frost, arm's warriors are easy to play.
PvE Fury is still the way you want to go, but Arms is up there too if you care. I typically tank in PvE and it's a blast on the warrior. Again, great tools, great mobility, rotations in pve are pretty easy to pick up as well. IMO easier to deal with than managing RP and runes on a DK.
They Solo old world content just fine especially with Second Wind, though they aren't the best at it. Fury is a good spec to use for the Bloodthirst heal. Prot does fine, and second wind eventually will save any spec in most situations if your HP gets down that low. Second wind truly is OP in certain situations, haha.
Overall, they are fun to play... but are easy to use and incredibly simple. High Mobility but also highly susceptible to kiting. Rage is a fantastic resource system in group pvp, and they become more powerful the more teammates they have supporting them, arguably moreso than any other class.
DK's are pretty much around the same level in just about everything. The runes and RP system are a bit more engaging. Frost is a bit more simpler than Unholy, but mostly due to the pet. They are just different playstyles. I like to think of it as sprinting vs jogging or Frost and Unholy respectively.
Frost brings little to the table besides burst and damage, but it does a good job at what it does. Unholy is more slower, setting up and pressure in other way's like more, and more powerful Necrotic strikes.
War's have better defensive cooldowns in pvp but like I said above DK's put out more damage/pressure. Outside of their pwn everyone killshot macro.
PvE, similar. DW frost is more in depth than 2h frost or Unholy, but rune/RP management will still be a little more to manage than just simply watching and spending rage. Tanking, I have noticed DK tanking is a bit more bursty, while the biggest difference is DK tanks do more dps, heal more due to a lack of a shield.
I decided to main my DK, just because I am drawn to the class more and I think it's more fun to play. Warrior mobility is a blast however, and quiet frankly I find them to be a bit too simple even with all their different tools. You no longer stance dance, and I am not a fan of the reckbomb macro, being on both sides of it.
Eh, hope that helps some.