Well I felt like it's time to weigh which party game kicks ass. So now I'd do a comparison on the more touchy areas than just the graphics and music because both game rock in those areas. Now here's my comparison:
Mortal Kombat Komplete Edition (as well as its previous version Mortal Kombat 2011) goes back to the realm of 2D style fighting meaning no nonsense sidestepping, it has a button for each limb quite similar to Tekken plus it has really accessible gameplay. Tekken 6 on the other hand retains the 3D movement which can sometimes be great but can also get annoying for some. However I do have a hard time judging which is better since they both have very different approaches- Tekken focuses on REAL martial arts and projectiles (if any) are NOT a spammer which makes Tekken 6 a little more accessible than Mortal Kombat 2011. For me, I'd give this a tie. But I would say both games are very accessible to noobs while having a deep playing system, not too deep as not to frustrate players while keeping it simple enough for beginners but not too simple to become a boring gameplay.
Both feature their story modes. So here's where I think I'm getting mixed. Tekken 6 features the seldom frustrating Scenario Campaign to which I wish was like MK Armageddon. In Mortal Kombat Komplete Edition, the story mode features an interactive movie but sadly you CANNOT skip the cutscenes which forces you to watch unlike in Tekken- however it focuses on purely kombat compared to that of MK Armageddon's story mode. For me, I definitely am mixed on both of them but I prefer MK Komplete Edition's story mode than Tekken 6's Scenario Campaign.
One Player Mode and VS. Mode:
So I'd focus on the one player mode between games. So as usual, MK does not have a story mode per character and it's pretty regularized. I would say that MK Komplete Edition does have a lot of coolness in the one player modes or the Konquest Tower which can be fun and frustrating. But I'd start to talk about the coming of the Arcade Mode which has the nostalgic value. So you fight seven random characters, an ultra cheap version of Shang Tsung (the old version) who morphs into any of the characters which the regular Shang Tsung can't, then either Goro or Kintaro before you fight the main man Shao Kahn. So pretty much, they're not playable which makes it fair considering how powerful the four cheap bosses are.
For the VS. Mode, you definitely will and will have the return of the Kombat Kodes. However to select a stage to fight in, you don't require yourself to enter a Kombat Kode to do so. There's a button to select and if you select each stage with Start except for a few, you get to hear the classic music. The VS Mode can be pretty entertaining in itself as well.
In one or two players, there is the Tag Team Mode which is sort of like Tekken Tag except you must beat both characters than just one of the characters. What I don't like with the Tag Team Mode is that you don't get Tekken's type of victory poses if you don't decide to do a fatality nor do you get to fight a tag team of Shang Tsung/Quan Chi then Goro/Kintaro then Shao Kahn with a random partner. To be honest, you are better off playing Tag Team Mode in VS. Mode.
I would readily admit Tekken 6's endings are better but I freaking hate having to play through Scenario Campaign to unlock them. What in the world is Namco thinking? Tekken 5 was better for me. For MK Komplete Edition, the endings are an animated narrative which kind of mimics Killer Instinct's endings with cell-shaded graphics. Tekken 6 still wins the quality of the endings but the Scenario Campaign is freaking painful. MK Komplete Edition still follows the traditional way of getting endings.