I've done both.
I try not to stop mid fight, but depending on the advneture and what the party does you just don't have a choice.
If I have to stop.....
I always stop at the end of a round.
Paper clip my Init cards in the correct order
Make notes on what NPC's have done / need to do
Take multiple pics of the board with the camera phone ( I actully think I have two or three games stored on it as we speak

)
Depending on the fight will also note locations on a paper map as well
Have everyone note status of HP, Spells up/used on a sticky
When we get started have everyone tak a couple min to review what then had done, and what spells they had put up for the party.
I'll give a quick recap of why they are where they are and what the goal is beyond surviving.
While running RttToEE I even had several fights that woud span 3 sessions, start one, take the entire next session and then finish sometime during the third.
Of course this only works if you are doing a weekly game and know you should be able to play the following week.
I have also just ended the night a little early instead of getting a round or two into the fight and then have to stop.
With something like this I think its really depends on the group and what the repercutions of playing that extra couple hours is going to have on the real world the next day.