The main limitations: (1) can't do the equivalent of ISOs and so the options you can grant will always be "non-qualified" (generating ordinary income on the "spread" at the time of exercise); (2) need to do custom drafting, with attendant expense, to mirror standard corporate tools in the LLC context (restricted unites in lieu of restricted stock, preferred units in lieu of preferred stock, etc.); (3) passive investors will wind up paying employment taxes on net income of the venture even though they are not employees (see the lively HN discussion comparing the LLC to the S Corp on this point, here http://news.ycombinator.com/item?id=1063516); and (4) for tax reasons related to their LPs, VCs can't invest in them.
Among the advantages: (1) more informality in management (normally by consensus among members, reflecting the LLC's strong partnership roots); (2) can get tax pass-through without needing to abide by S Corp limitations (with S, can have only one class of stock, can't have foreign shareholders, can't generally have entity shareholders - all of which you can have with an LLC and still get the tax pass-through); (3) can do specialized allocation of losses, which is an important factor for certain investors; (4) can grant profits-only interest to key founders who would otherwise take big tax hit in taking significant equity in an established, high-value startup.
The biggest practical advantage of an LLC is also its biggest practical limitation, and that is that it is like the siren song tempting founders to do quickie, online setups for their startups "just to get started." This is fine for some purposes but can lead to problems if founders use their startup kits to fill out standard templates without taking proper precautions to protect their IP (by failing to capture it for the company), to protect their equity structure (by making sure that founders have to earn their equity over time), etc. In my experience, most of these situations work out without problems but it is wise to get an initial legal consultation in such cases to make sure that, if you take the attendant risks, you do so with open eyes.