The basic form of the game is a sandbox, 4X starting from just your homeworld. that's what most people spend most of their time on. The 2 story campaigns are just color, background, and a certain amount of "solve this situation - using the usual rules of the larger game" puzzle effect.
There are substantial differences from DL to DA in detailed development play. There are also some important changes in how combat is resolved, but you might not realize those until you ar playing with bigger ships/fleets later in the game. There is also at least one bug in combat in DA that adds to the current differences enough to affect ship design choices; it doesn't completely break play (its still a great game) but it was unintended and is expected to be fixed/tweaked hard in the final version 1.6 (see discussions in the forums of the Off-Type Defense Bug).
Most people seem to stick with DA over DL once they switch over. There are some additional factors to play with in development of systems, and the Super Abilities, etc. Personally, I would suggest playing a month or so with DL, then go to DA, jsut to give yourself a ramp up effect.
This is esspecially so if you intend to eventually play the 2 story campaigns, because the DL campaign uses the DL engine/rules, and you will want to be familiar with the differences.
One thing I will point out that is a bit subtle and not especially documented (except in forum discussions). In DA, marginal quality planets are WAY more important than in DL. This is because the effects of terraforming are essentially reversed between the two versions. In DL, high PQ planets benefit rather more from the various terraforming techniques than low PQ, gaining a larger number of playable areas. In DA, all planets above about PQ6 gain a little from each stage of terraforming, but low PQ planets gain huge jumps in usable territory. And the AI does not exploit this well (though they are generally better than you at initial planet grabbing.)
Enjoy,
drrider