There didn't seem to be a lot of clear information out there when I was looking to buy mine (quite some time ago now), so I had to do a lot of digging to find out the exact differences between versions, as there's three versions of the drop ship available, and two versions of the APC, and the details of each aren't exactly well documented for some reason. Perhaps because these were made primarily for the Japanese market.
Here's a basic rundown.
The Drop Ship comes in three variants, the 01, the 02, and the 03. The variations between each are so:
The 01 (Standard Edition) is based on the first Drop Ship you see in the Aliens film, and as such it has a unique 'Bug Stompers' ship logo decal under the cockpit, pilot in the seat of the cockpit, has a 'weathered' paintjob (which basically equates to some black 'scorch' marks over a slightly darker/grimier green paintjob compared to the 02 version), as well as 01 ship markings, and comes with a mini (to scale) Alien Warrior pack in.
The 02 (Limited Edition) seems to be the one that is most easily available these days, and is based on the second drop ship that Bishop remote pilots down to the colony. It has its own unique 'Smart Ass' logo decal, has no pilot in the cockpit, has a 'clean' version of the military green paintwork (slightly lighter green than the 01), as well as the obvious 02 markings, and comes with a scaled Alien Queen pack in.
The 03 (Exclusive) is by far the rarest and hardest/most expensive to find (apparently limited to 500 worldwide), and is Aoshima's own custom paint variant. It has clean black body paint, pilot (like the 01), the 'Bug Stompers' custom ship decal (same as the 01), and the Alien Queen pack in (from the 02), as well as its 03 markings, of course. So basically it's pretty much the same as the 01 version, just painted 'stealth ops' black, and with the Alien Queen pack in and 03 markings added.
All versions have openable wings and weapons mounts, as well as switch out parts for displaying landing gear as either retracted or open, along with an openable ramp underneath the ship, which the APC can fit into (and yes, it does hold closed in place with the apc inside). The majority of the body is made of die cast, with some plastic parts, such as the ramp, cockpit windows, and a few other bits and pieces.
As for the APC's, the two variants are pretty much identical, except for the pack ins.
The 'Limited Edition' APC comes with a mini Alien Warrior pack in, the same as you get with the 01 drop ship.
The 'Standard Edition' APC comes with 2 mini Colonial Marines as packs in.
Personally at the scale, the Alien looks far better than the marines do, but given that the Alien is only 3cm high or so, and the marines smaller than that, the fact is you were never going to get something ultra detailed at such a tiny scale. That said, they actually did about as well with the Aliens as one could hope for, considering the obvious limitations. The Marines, again, yeah, no so much, but it is what it is...
The APC is pretty much all die cast, except for the two movable gun mounts, and the wheels.
Personally, as a big Alien fan, and someone who likes die cast replicas like this, I like mine quite a bit, and think the paint is fine on each version, as far as a factory piece like this goes. But like with just about any retail piece, well done custom paints can improve just about any factory job. Mind you, I got my Drop Ship and APC for a pretty good price direct from Japan too, so that always helps.
Hope that helps.