Does steeping the same amount of tea in different volumes of water lead to the same or more caffeine?
TLDR: Yes.

The amount of difference is a complicated question as there are many variables involved. There is an osmotic pressure differential and there is also an equilibrium that will be reached between the tea compounds in the leaves and the water, so technically speaking tea steeped in more water will have more caffeine and other compounds, but there are many factors that will affect how much more. 

To do an experiment correctly you'd need to have two bags with the same concentration of tea per volume unit and the same surface area exposed to the water and two cups of the same size and material with the same amount of water at the same temperature. Putting a tea bag into a larger vessel will introduce other factors (such as fluid dynamics and temperature). 

Here are some of the variables that would have to be taken into account:


volume of water 
temperature of water 
surface area of tea:water
turbulence of water
type of tea
pH and other chemical properties of water
infusion time
surface area of water:volume of water
permeability of tea bag (if any)
type of tea
loose leaves vs in a bag; stirred loose leaves vs. clumped loose leaves