Let's meet one more time is when you want to meet a person which you won't be seeing again soon. Let's meet another time is when you can't see this person at this moment and you want to delay the meeting for another day I hope this makes sense :)

"one more time" means that the next time you meet will be the last time. "another time" means that you will meet at least "one more time" and possibly more.

Let's meet one more time. Встретимся ещё раз. Let's meet another time. Встретимся в другой раз.