As the title says, what would be a good way to farm prestige? Just grind the bgs and arenas or do WQ's or both? The main reason I want to level up my prestige is to get the mounts, so I would like to know an efficient way to do so.
The most efficient way is would be constantly winning rated arena matches. However this is highly unlikely since at one point you'll reach a rating where constantly winning is close to impossible.
So the options listed here are your preferred strategy (in order of efficiency).
Those can earn you the most honor for how little time they need to complete.
Unfortunately there's only 3 tower quests (300 honor) every 24 hours. There are also the arena quests which are done rather quickly (500 honor) but they also only spawn every 6 hours.
So what should you do after that?
First win of the day!
Make sure you'll get the first win of the day for every queue there is. Battleground wins will give you more honor than arenas and rated will reward you with more than unrated matches (the rating doesn't matter here).
Now you've completed every worldquest and you've won at least once in every queue available to you? Now there's only one option left:
Ok we all know that zerging in BGs is bad and you shouldn't do this if you want to win. Unfortunately it's still the most efficient way of grinding honor after you've completed all the other options. Note that while this is faster than "properly" playing the objectives in BG it's not an insane difference.