I'm not positive there was ever a 1.5 of DA-that would seem to be DL. If there was a DA 1.5, it was before my time.
If you are on DL, the amount of changes you're looking at are even more so than what I've listed. The primary differences between DL and DA are a slightly tweaked economic model (DA planets make less money than DL planets), the espionage system change that allows spies to disable planetary improvements, engines taking up more space and costing more as components, extreme environment habitable planets, which require tech research to colonize and more tech research to properly use, and racial super abilities, of which the most notable are breeder (8x pop growth instead of 2x at 100% approval), hive (25% cost factories), diplomat (large diplomacy/influence boost and can speak to races every 4 weeks as opposed to every 8 weeks, which is a DA/TA rule), and annihilator (can build a spore ship to invade enemy worlds without troops, kills off all the population and turns it into a toxic world).
There's also the fact that industrial/research production decreases somewhat on a per-improvement basis and maintenance increases somewhat as well when going from DL to DA.
Latest version of DA is 2.0, and before that 1.8. The primary difference between the two is that 2.0 backports TA's changed espionage system (civ-level for espionage, but keeps planetary for disabling improvements-this has the side effect of being able to spy on minor races), although with 2.0 DA is now compiled using floating point precision, which means you shouldn't encounter any more military/social production rounding errors (thank Cari for that).
DA is faster than TA in a sense, in that it takes somewhat longer to get through the new tech trees to the same point in the old tree. TA is faster than DA for weapons-probably still, even with the +50% cost added in-as the trees were redesigned and don't have all of the techs from DA, not to mention cost much, much less. Armor, on the other hand, remains almost the same.
TA changes a lot. You have the new tech trees to choose from, you have a base speed of 2pc/wk as opposed to DL/DA's 1pc/wk, you have 8mt/wk from a starting colony whereas DL/DA are 6mt/wk, and the production of an initial colony has changed as well, to 14 research/14 industrial (was 16 industrial/10 research in DA-don't remember what it was in DL). Thalans don't get farms in their tree, some races are missing some invasion tactics, Drengin/Korath don't get counter espionage centers-but are the only ones who get mini-soldiers. The Yor don't have government, and their morale buildings are part of their farm buildings. They also don't get a spammable economic building.
And, as always, with each new expansion industrial/research output decreases somewhat and maintenance increases somewhat.
One other thing to watch for in TA is the focus mechanism-it was changed in TA so that only 80% of what you lose is given to the focused production-or, if you prefer, 20% of the whole rather than 25%.
In addition, due to the tech tree changes, most races (except Terran, Arcean, and minor races) miss out on 57 morale from trade goods and techs. While some races make some of this back (Altarians/Drath get 20 from techs), everyone else is limited in the morale improvements they can build in their trees, generally to a 25% improvement, whereas Terrans/Arceans/minor races can build a 40% improvement. Torians don't get any tree bonuses, but can build a 50% improvement, so it roughly evens out in that regard for them.
The Korx and the Krynn are the most hurt by this change, as the Korx only have a single morale building that they can build, one per planet, at 25%, whereas the Krynn have two one-per-planet buildings that total 50% (20+30). All other races can at least spam their morale buildings if they feel the need.
This all leads to a reduction in the amount of people you can comfortably sustain on one planet-the TA rule for non-Terran/non-Arcean/non-minor race would appear to be one farm for initial colonies and no farms (nor even a food distribution center) for civilization capitals (homeworlds).
TA also brings, with 2.x, the ability to select the frequency of random events and extreme habitable worlds in your galaxy. Another TA 2.x change is enabling/disabling tech brokering-so you have the option of only being able to trade what you research (and all the AIs are limited by this rule as well).
There's a lot that I've missed, but I'm still a DA player at heart, so someone else would be more helpful.