Stazro : Against Persia, I always follow the same war pattern :
1 - one war of unit attrition during the first century bc where I take only Ninive and Ctesiphon or so.
After this war, Persia will begin to regularly send Mesopotamian Bellatores at your cities, which is a good thing, since these units are very often used to attack right away. So instead of hoarding units and increasing his power very fast, the growth is actually subdued by the creation of those HN units as they are destroyed fairly regularly.
2 - One real war after I've finished all the normal conquests (Gaul, Britain, couple of Germanic cities, Dacia) which normally happens around 200 ad (which is perfect timing for the Germanics and Huns are still no big threat by this time as they do not yet have any unit spawning wonder.) In that war, the crucial one, I begin normally by letting Persia's offensive unit attack me and be killed and, when he's naked, I charge forward and take at least Bassora, Susa, Hamadan and Siraf. It doesn't take that long because, by then, Persia doesn't have an army anymore and it's just a matter of patience. Bombard, hit point attrition and using elite eques legionnarius who will in most cases retreat when they reach 1 hp, all in order to hurt as much as possible the Praesidium Parthicum. The time it takes is reasonable. Perhaps, if I remember correctly, 4-5 turns of bombard skirmish for cities with 1 Praesidium Parthicum and 8-10 turns for cities with 2.
When you have taken those cities, you can make peace and get 1 or 2 (if you don't houserule against that in your game) and Persia is essentially broken. And it is not dangerous to have your whole army there if, like I mentioned, you're fresh out of a war with Germanics and they don't have their uber units yet.
3 - Then, later, after another unit attrition war against Germania, (no set date as it varies too much, can be in 350 or in 450) you can go back to Persia and finish the job by taking Ecbatana, Ispahan, Rhagae, Tara... Using the same pattern, it is still long, but very much doable. The only impossible to conquer city is Persepolis : 3 uber defenders make it impossible, unless you have a lot of time and something like 60 catapults.
As it afterwards destroy any threat in the east and free all your units for the vital fights against the Germanics and Huns, it is well worth the trouble and I heartily recommend it to all players.