Capital Ships have hyperdrives, Escorts do not.
Hyperdrives are huge expenses, requiring a great many rare elements in their construction, so a Capital Ship is a massive commitment of Imperial resources. However, a Hyperdrive projects a space-warping field for some distance in every direction around the equipped ship, so any Capital Ship is capable of "towing" a number of Escorts with it as a support fleet. Some Capital Ships are carriers, and contain many additional internal parasite craft (fighters, etc). It's possible that the number or total tonnage of Escorts that a Capital Ship can tow is proportional to the size of the Capital Ship; I haven't decided yet. I would recommend having a hard cap of, say, 50 Capital Ships per empire. However, there should be soft caps and disincentives for large Admiralties built into the game design so that the hard cap is almost never reached in practice - the game shouldn't *feel* as though there is a hard cap towards which you need to race.
Another FTL option is Subspace engines. Subspace engines are cheap and easy to build, but no sentient lifeform can survive travel via Subspace unharmed (insanity or death result). These ships are used for automated cargo vessels for redistributing minerals, supplying fleets, etc. Troops and colonists have to travel with a Hyperdrive-equipped fleet. (This is a just a background sanity-check to make the economy and resupply rules logical - I wouldn't expect subspace ships to be directly shown on the map, or directly affect play in any way). Subspace engines might also used for powering missiles or long-range bombardment weapons - neatly justifying FTL projectile weapons in combat.

Capital ships have a fairly detailed design process (which I'll leave unspecified for now - there's many possible options). You're not expected to control very many, so each one takes on the role of an Admiral as well as a "unit". They earn XP in combat and might possibly gain Traditions based on their history of performance - this would be similar to Total War's Virtue/Vice system. Capital Ships would be infrequently built, but quite frequently refitted. "Refitting" a Capital Ship can sometimes be a very extensive process, including even changing the size class entirely - this represents taking out the expensive hyperdrive core and rebuilding a new vessel around it, transferring the crew to the new vessel. This would allow you to maintain the Traditions of an old vessel while still keeping it useful in the later game. Alternatively, we could simply say that when you build a new Capital Ship and give it the same name as a ship you once had, it inherits some of the Traditions and XP of the original ship. Traditions could include things like "Bleeding Edge" for a ship that is frequently refitted with SOTA tech or "Glorious Valor" for a ship with a history of charging into combat, or even negative Traditions like "Botched Repairs" for a ship that gets near-destroyed.
Capital ships become tactical interest points in the battles, because they are so strategically important. Capital ships would also be the only ships that carry player-activated Special Equipment. This category would include things like Black Hole Generators, etc - special weapons with unusual effects that the player has to specifically activate for them to be used.
Escorts have a very simple, streamlined design process. They are built in Squadrons (similar to Total War's "Units") of at least 10, maybe up to 100 or more ships per Squadron. My preferred system for Escort Ship design is a process of choosing priorities in the various areas of space-ship competence; the ships are henceforth automatically refitted with the best equipment your Empire has available, in keeping with the specified design priorities. (Priority choices would be things like Missile, Beam, Fighters, Point Defense, Speed, Shield/Armour, Stealth). That reduces micromanagement of your "regular troop" units. With regard to Special Equipment, Escorts would mount only passive gear which is always in effect. Background-wise, this can be justified by saying that the player-activated Special Equipment has extraordinary power requirements that can only be satisfied by Capital Ship systems. This further reduces player micro-management of Escort ships and further emphasizes the tactical importance of the Capital Ships. Thus, Escort Ships must be deployed and maneuvered cunningly for maximum effectiveness.
In combat, Escorts can be assigned to guard a Capital Ship or roam the battlefield as an independent unit. Escorts form the bulk of a given fleet's force, but are individually weak compared to a Capital Ship.
By default, each Capital Ship heads its own Task Force of Escorts. Multiple Capital Ships can be formed into a single Task Force and their associated Escorts merged into a single pool. Splitting a multi-Capital Task Force into components will require a dialog box, but that's not hard to achieve. In a multiple-Capital Ship Task Force, the largest Capital Ship is the flag vessel (ie has overall command). This may or may not be relevant depending on whether we track morale or command/control bonuses.
Escorts can be assigned to a System or to a Capital Ship-led Task Force; when built, they are by default assigned to the System Defence Fleet in the system where they were constructed. They can then be transfered to any of your Task Forces that moves into the system. With regard to the Strategic Map UI, there should be different icons for a System Defence Fleet (Escorts only in a system) versus a Task Force (Capital Ship(s) + Escorts). There should be a simple drag-and-drop interface for moving Escorts from one Task Force to another within the same system or to the System Defence Fleet in that system.
We could possibly have Orion Artifacts that can be built into Capital Ship systems; these could grant passive bonuses or possibly emulate advanced player-activated equipment. Some might even be utterly unique. Orion Artifacts would be effectively indestructable; if a ship with one is destroyed, the Artifact is salvaged by the battle's winner. If there is no winner or a Space Monster wins, the Artifact remains in the system for a future claimant. I would prefer not to have recruitable "personalities" in the MoO II sense for Capital Ship captains; it would be better for the ships to have names and take on personalities in their own right. MoO II Heroes were bad for the game because it introduced a very random element that could have large influence on the game (ie, which Heroes you were offered).