There are 2 gyms, side-by-side

Of course I'll take down the enemy one. Takes minimum effort to select a battle team and no dodging required (6 vs 3

If the turnover is high anyway, then there's no point prestiging the other one in hope that you'll help your team keep it in a high traffic area.

Both.

You can take both, just beat the enemy one till one or two pkmn, then shave your team, and beat enemy gym till the end, easy

I would prestige the friendly gym first, very easy to get 4-5k prestige on a single round, only 1 fight needed to level it up because it is level 6, while the level 3 enemy you have to battle twice at least, even 3 times if it is close to level 4.

After placing a mon on the friendly gym that is now level 7 I would take down the enemy one, no one will take down the level 7 on the time you take down a level 3, so you have more than enough time to claim the coins.

Take them both down. If you joined Team Mystic, we are on the same team. If not, I don't care..lol

I'd take down the L3. Collect my coins then power up the other and drop a critter in expecting the new L3 gym will change hands in short order.

Prestige lvl 6 friendly gym.

If I'm done and no one is attcking it yet: move on, defeat the enemy gym, leave a 10 CP pidgey and collect 20 coins.

If' I'm done and someone comes to attack it while moving to the enemy one: wait the guy to finish and take it back. Keep doing this if the other guy keep taking gym down until one of us need to go.

If it's me who need to go: collect the 10 coins and go home.

If its him who go away: move to enemy gym, take it down, leave a 10 CP pidgey there and collect the 20 coins.

Depends on current traffic, are both gyms being battled by others currently or do I have 15 minutes to get what I need done?

High traffic currently means I would take enemy gym with low CP throwaway, collect, and transfer it when it comes back in the next minute or so.

If I have some breathing room I would first prestige the Ally gym and stick something like a Snorlax in there for a time buffer then take enemy gym for attempt at 20 coins more.

It depends on if I am ready to collect immediately, or if I need to hold up an hour or two. I would attack both; but I would prestige the friendly first if I wasn't collecting right away. Otherwise, I would attack the enemy, collect, then prestige and hope the other teams were napping that day.

For the good of the team will be to take down lvl 3 because for a while 2 team mates will spent only 10 seconds to collect 10 more coins.
Also this way another team member that needs 2 more gyms will only have to prestige 4k for lvl 7 ad oposed to 8k for lvl 8. This takes into consideration that you already had 9 gyms prior to arriving there since you said you only need one more gym.

If your time is more important, I still think beating lvl 3 gym on two rounds is faster.

All the above took into consideration that the time span before gym changes is a few hours since you said they change hands. So no advantage to make your team gym stronger, only disadvantages(longer prestige time for next player and minus one spot for aa potential 4th team member.

Take down enemy gym and put my best defender in, level up friendly gym and put high-CP mon in, if I have potions and revives to burn level up friendly gym further

Prestiege first, then take the other one too.

Neither, why waste your time on constantly changing gyms. Find stable gyms!

Neither, why waste your time on constantly changing gyms. Find stable gyms!

Level one gym and leave the other. Taking down the other brings no benefit for anyone- you use your potions and revives, somebody else will use his potions and revives to take it back.
With just training the own gym and leaving the other, you live and let the others live too. In a war of attrition, nobody can win. Live and let them live, is aiming for win-win-situation.

If you have some time and ressources left after harvesting your 100 coins, maybe training the own gym a little higher to prepare it for the next defender would be really great.