Each Battleship works well in a certain role, and is a challenge to fit for extremely different roles. The Abaddon is a close range brawling monster - huge damage (1000dps at close range) using Pulse Lasers with a huge buffer tank (150-200k EHP is not uncommon) designed to wade into a fight, supported by logistics and really hurt things as part of a fleet. It’s rather Amarrian really.
It’s not a good mission ship - not in the “long range, active tank” common flavour of mission ships. I’ve used an active tank Pulse Abaddon for missions and it’s hard work (40-50km with Scorch as I recall), you end up plodding around trying to close range on targets and worrying about capacitor.
So saying, if you can catch up with them you can hit them really hard!
The Apocalyse is the normal T1 Mission Amarr battleship - it’ll take Mega Beam lasers and a reasonable active tank - The range bonus directly translates to damage for Energy Turrets as you can easily use Pulse Lasers instead of Beams and flip to higher damage crystals as the fight evolves. It’s a nice medium to longer range battleship as well, but even that will struggle to fit Tachyons.
The real problem is the Tachyons - they are not a general purpose weapon. They have specialist uses where the range is important or there are fitting bonuses that mitigate their fitting costs as @Chainsaw_Plankton commented, and @Kannibal_Kane is right about the tracking; you ain’t going to hit things easily). But even then, to gain their advantage you have to trade off something else (tank normally) - but that is Eve for you: Where in the triangle of Firepower/Speed/Defence do you want to be?
If you’ve trained Tachyon IIs, which means you have Large Energy Turret V already, then training T2 Large Pulse Lasers is going to take you minutes - may be a day to get a few percent more damage.