It's obvious snyper won this, and it should be obvious *why* he won, so instead of wasting time explaining that, I'ma give a short critique of Atticus' verse for his benefit.

"My name is greek" -- Irrelevant, since you didn't spin this into any kind of wordplay.
"atticus brings snyper the grief" -- Filler. Leave it out unless you need it for a complex rhyme scheme.
"market PDI saw the disease / So how could snype possibly handle THIS BEEF?" -- Okay, here's one concept you turned into a punchline. It'd be tighter if you reworded it though.
"I'm snipe'n snyper from 90 thoughts up" -- A personal, which is good, and a metaphor "90 thoughts up" which is also pretty good.
"Not on my level cuz U lower than 'dirty pots' / and I'm higher than 'shiney cups' / talkin shit in ghetto / better leg it out my 'grimey cuts' " -- Strange references that I didn't really get, unless dirty pots are toilet bowls and shiny cups are trophies or something like that. You seem to have a concept in mind but aren't expressing it too clearly. Also I don't get your slang like "grimey cuts", but that could be my fault.
"Mellow head better frollic back 2 his meadow " -- The idea is okay, but even using words like "frolic" and "meadow" seems to soften the feel of your battle verse. This would work better if you'd just thrown a really hard punch and *shown* that your opponent is soft enough to earn those descriptive words.
"Im surrounded by demons " -- Just fodder for the comeback, which Snyper didn't even need to use.
"Snype the only thing u shootin is leakin super soakers / wit ya man super soldiers semen" -- Another personal; the first line was alright but the second one sounded awkward (does Snype have a crewmate called "super soldier"?).
"told his girl snype like skeet skirt " -- Another slang ref I didn't get.
"but the bitch don't believe it / so in ya hands my erect dick I'mma leave it " -- Doesn't make enough sense to come off as hard as you intended.

Okay, hope that was helpful. Vote = snyper, if I didn't already make that obvious.