I'm not sure what your background is, but I can understand wanting as close to a real M4 as possible, because I carry one, so I like the idea of having as close as a private citizen can have, not just for platform continuity, but because it makes me happy.
That said, it's gonna have to be your call as to which is closer. Assuming you mean 16" barrels:
Colt is, of course, the OEM manufacturer for the M4 Carbine, but from front to back:
A Colt barrel will be closer, and will be marked like the USGI part, and the FSB will be "F" marked. I'm not sure how LMT barrels are marked, but their FSB's, while the same height, are not "F" marked, as LMT only makes them in one size, and doesn't need to distinguish them.
Colt will also have the OEM side sling swivel, which I believe is not standard on the LMT. Furthermore, without debating whether or not it's necessary, the Colt will be parked under the FSB where the LMT will not.
The handguards, obviously, Colt will have the OEM parts, however few M4's I see issued ever have the handguards anyways, most are equipped with a KAC RAS.
The upper receiver, again, the Colt will be more "correctly" marked, with the M4 above the gas tube hole, as well as the "C" mark next to the forge marking on the upper.
Rear sights... carry handles will be more or less similar, if you elect for them, but the most prolific sight I've seen issued lately, and at least all around country in Afghanistan is the MATECH, hands down.
BCG will be OEM Colt.
Lower receiver, here, I would actually tend with LMT as being closer. LMT uses the standard mil-spec trigger pins, unlike the oversized pins on the Colt rifles. Furthermore, IIRC, LMT's can be purchased without the LEO markings (I may be wrong on that...), and the rollmarks on any Colt rifle are different enough, unless you get an MT6400C lower, and possibly not even then. However, the Colt will again, be a Colt. However, the "pony" marking is even different than the USGI ones, much bigger and gaudier on Civi rifles.
As far as the stock goes, the buffer tube supplied by LMT is slightly different, and offered in five or six? positions, rather than the four of the Colt. Also, the Colt stock will be the USGI part.
And that's that, however, an LMT is pretty damn close, and from all accounts are excellent rifles. I'd take heed of what others have said, that milspec usually doesn't matter, and certainly doesn't always mean better. I hope I answered your question straightforward, though.
Me personally? I went with a Colt mixmaster, built out of parts, but all OEM on an MT6400C lower. And I think my return home present is going to have to be a LE6921, as well. Otherwise though, you'll have fun with whatever you choose.
HTH,
~Augee