All else held equal, does a pot of tea have more total caffeine than a mug?
The pot will have more caffeine. 

You are right that the concentration of the final solution is determined not only by steeping time, temperature, etc., but also by the amount of water available to dilute the stuff coming out of the tea, including caffeine. It will reach balance earlier with less water. So more water will get more of the different compounds in tea dissolved. 

For an empirical observation by somebody surprised by the result, see also this question.