I find that purchasing cap ship levels can work early game for a TEC carrier blockade rush. Acquires extra strike squad and another level of blockade. Horribly expensive, but hopefully you can sack your enemy for a comparable amount of funds.

I sometimes purchase the levels if I think it's going to be critical to my survival. Usually further into the game I'll have researched Mass Transcendence though, so they auto-level to 4 pretty quickly.

Purchasing upgrades later in the game when your credit income is 30+ can be helpful if you want a pair of cap ships in a fleet. Multiple cap ships in the same gravity well share experience, making all of them level slower as you add additional capital ships.

In most cases though, you'll want to have one main capital ship at as high a level as possible. A level 10 capital ship with military research done is usually 3 times stronger in all stats(health, damage, regeneration, etc.) than a level 1 ship with no research at all. This can make them nigh-invincible outside of massed focus fire.