Woah woah woah!!! This is what I was MEANT FOR.
It's basically a lighter Virtua Fighter. Trust me, you play both side-by-side, especially going back to the first DOA, and it's eerie. Identical button layout and there's smiliarities in their "ring-out" mechanic. This isn't a funny coincidence, or copycat syndrome: Yu Suzuki helped Team Ninja build the original DOA. There's a lot of mutual love between the teams; The VF5 guest chartacters arrived in DOA5 free of charge, or at least that's what Team Ninja's current director says.
Lighter's a not particularly "fair" assessment. Virtua Fighter is a FRIGHTENINGLY deep fighter. They shot off into the expert pool ages ago, and you're gonna need to learn to swim QUICK in those waters. You know a fighting game is technical when character guides don't start with combos, but with FRAME COUNTS. And that's ignoring the fact that the effects of your moves are actually affected by the FOOT STANCE of each fighter, respectively to one another.
I'm think I'm a moderate-level fighter. I'm not even vaguely tourney-worthy, but I have all the staples downpact for any of my Tekken characters (read: Alisa 'n Lili). Tekken is just technical enough to look impressive while still having enough mash-friendliness.
DOA is a lighter fighter than either, but not for nothin', it's also the quickest at making you feel competent. If you've ever had the frustration of being beaten by someone because you're better, but still nowhere near good enough to take on a masher, and you don't feel like spending a couple hours on Tekken Zaibatsu giving your character of choice some "teeth", DOA is probably the game for you. Once you have the counter system down-pact (there's in-game tutorials tied to the storyline for this), you can wreck people pretty quickly.
TL;DR?
DOA - Light, easy faire, but figure out how to counter
Tekken - A step up in complexity, if you don't mind juggling folks by their ankles
VF - Beyond here lie dragons
One last note: I'll tell you straight-up, I'm a DOA whore. About the only fighter I value higher is Smash. It's gotten monumentally better in each itteration, though there seems to be an internal and external tug-of-war regarding the more "exploity" themes.
In DOA2, the boobs jiggled like a six pound jello brick, the amount of time you had to execute a counter could be measured in SECONDS, and a counter would eat a quarter (no joke) of your life bar. In DOA5, they jiggle's minimal, counters have split-second windows, and you're only gonna tear through a health bar if you earned it.
If you're looking to dip in, you might wanna wait for them to announce a Wii U version of 5 Ultimate (due out this fall). Barring that, look for a sale on the DS "Dimensions" game (good for getting up to date with the story, for whatever it's worth (not much)) or the PS3/Xbox 360 version of 5.
If anyone's experiencing frustration with the combat system, drop me a line here, I'll try to help.