What was the effect of the Roman Empire being able to tax enough to support its army upon its populace? With medieval governments being smaller than the Roman one, did that mean a peasant in medieval Europe was taxed more lightly and was economically better off than his Roman counterparts? Or, was the Empire able to tax the wealthy more effectively, or have a more productive economy due to the sort-of globalization inside the Roman world? Or, did medieval taxes just support nobility lifestyles?

The main effect seems to have been a great deal of internal economic growth and peace, as we can see from the fact that Roman cities grew in size but didn’t build walls until the crisis of the third century.

In terms of your second question, I lean more towards the effective taxation of the wealthy angle (at least at the height of the Empire’s power), as medieval taxes tended to have higher rates and more regressive forms to make up for the fact that the medieval state often didn’t tax the wealthy effectively. 

Calculating GDP per capita in premodern eras is extremely difficult, but it does seem as if there was decline or stagnation at best in living standards between 1 AD and 1000 AD, with a slow recovery during the High and Late Middle Ages, which picked up steam during the Renaissance and Early Modern eras, and then really took off following the Industrial Revolution.