It's probably Berserker. Engineer has stuff like cannons, minions, shield mixed in it's skill tree along with 2handed weapons. Didn't play Berserker much but I think his skill tree is all about melee dps.
Been playing duo as a Berserker with an Engineer since the beginning and we're both level 40 now. We both specced for melee damage basically, him with 2Hers and me with dual wielding, of course maybe that wasn't the most balanced or logical choice for multiplayer but it's what we both wanted to do, and we've been having fun. I have to say we both certainly hold our own roughly equally but he's superior at AoE (which is EXTREMELY important in this game) and I'm superior for single target combat, especially the super-strong bosses, which needless to say is also extremely important. Not that we don't help each other out -- I have various debuffs and just recently grabbed Battle Standard (or whatever the flag-drop ability's called) and he has his aegis bubble and such, but overall we're kind of doing our own thing, with me preferring to take out the biggest or most dangerous targets first while he mops up the trash. Worth bringing up may be the fact that even when I choose not to use claw-type weapons my class doesn't feel like it was really "meant" for AoE as much as other classes, though there are AoE-ish skills and a neat passive that makes my crits spill over to nearby enemies I'm not sure there's too much true Berserker AoE except that skill that binds enemies' souls together or whatever in the Shadow tree and probably the Tundra tree (which seems more like a caster berzerker to me).
Also interesting to note, even though my engineer friend is much tankier than I am, I still manage to survive extremely well just on high attack speed, high crit rate and charge build with the crit = lifesteal passive, and lifesteal on my weapons whenever possible, plus the ghost wolf summon when I can have him up (which is most the time, now).
tl;dr: They're both really great melee DPS but in my experience Engineer is more AoE while Berserker is raw single-target destruction; also the Engineer tends to be tankier and the Zerker more of a glass cannon though that can be taken care of easily.