The "limited edition," as it turns out, is simply the normal release with some extra free content for early adopters. Buying the limited edition (which, according to statements given to Shacknews, is a separate SKU despite the identical price) grants an exclusive gun, the MP7, and early access to two shotguns, the TOZ-194 and 870MC2, that normally require higher ranks. You can get your first look at these weapons after the break, unless you're a real Tier 1 Operator, in which case you've seen them.
[Update: The post originally included an erroneous reference to pre-ordering. Also, the status of the LE as a separate SKU from the original has been noted.]