Overall just plain L4 security missions Gila. Has the added bonus of being meta for Abyss runs as well as other uses. Doesn’t do full clears as fast as battleships, and can not solo epic arcs unless you multibox or duo, but vast majority of missions you pick up will not be the big ones, they will be medium or even small sized and battleships lose too much time due to their clunkiness on doing these on per time basis. Does require some active gameplay, you will have to learn how to manage drone agro as well as their ranges and other aspects and how to somewhat decent speed tank on some of the content.
Best T3C is Loki. HAM + armor or HAM + shield both work very well. Tengu a bit below that because its main damage bonus is kinetic so it doesn’t do as well as Loki vs targets that are resistant to kinetic damage. T3Cs also open up other PvE options to you such as the ones that require some scanning or hacking and they do so better then Stratios.
Most fun, Vedmak, hands down, no other ship currently in the game is as fun to do L4 sec missions in as a Vedmak, by far leaps and bounds. But its not optimal ISK wise and requires some fancy flying, a lot of speed + transversal tanking while retaining short range on your targets.
Drekavac is 2nd best on the fun list and has the added bonus of being actually very useful for fleets. It has armor and DPS of a T1 Battleship but is a lot less clunky and you can have a command burst on it. Though it requires a very active playstyle due to its weapon range while using Occult.
Most reliable for soloing tougher L4 content such as Angel Extravaganza bonus room and epic arcs, double prop Navy Scorpion with cruise missiles. It has 8 mids allowing it to have a very high tank and still retain double prop. Double prop utility is huge for a Battleship. You can get slightly better tank on other battleships, but then you have to sacrifice either the double prop or DPS application making it not worth it.
Best on average big mission full clears, Rattlesnake. Just your average cruise or HRML + drones. Cruise + drones you will be mostly range tanking everything, while RHML + drones has better application, better raw DPS and bigger tank for more brawling style. Both variants are good.
Ravens, Navy Scorp, Nightmares, bunch of other Battleships do OK and are comparable coming in and out at various situations but yielding same average results, exception being the Navy Scorp with its extra tank.
Burners are in their own category and there are several big threads on them that you should really check out if you intent to do them.
Best for lazy play for L4s, Golem. For me its too slow and so clunky it is absolutely not even remotely worth it, but some people like it.