Caffeine (a xanthine) is what's doing the stimualtory duty in coffee, but tea contains another xanthine too called theophylline used sometimes is used as an asthma palliative. Tea doesn't contain loads oh theophylline in fact usually not much, but if you start creating these 'superbrews' by steeping a load of teabags in a pan you can end up with a larger dose of theophyline that you might care for.
I've had this discussion with Biochem bods before and stuff and they come out with lines like 'theophylline won't affect you at the dosages contained in tea'. But the point they miss is theophylline has a narrow therapeutic range and high interindividual pharmacokinetic variability. In English this means that it effects everyone differently.
If you are the sort of person who goes off on one after a few too many cups of tea you are more susceptible to the effects of theophylline and probably caffeine too.
Onto coffee, I have more bad news, instant coffee certainly gives me anxiety rather than freshly prepared coffees. I'm not sure exactly why though, but I think that the beans used in instant coffee are inconsistant and generally of lower quality than beans used for making filter coffee and contain undesirable residues from harvesting. I should really investigate this to find out.
Coffee presses are pretty much the worse way to prepare coffee. A perculator with paper coffee filters will take out the lumps of coffee solids but also will remove the oils present in coffee which contain alcohols called diterpenes.
A coffee press does NOT remove the oils and subsequently these diterpenes.
These diterpenes along with some other chemicals have the ability to raise levels of alanine aminotransferase.
Alanine aminotranferase levels in elevation point to stress on the hepatic (liver) system. They can as much as double if you regularly slurp 'pressed coffee' Secondary effects of diterpines are increases on LDL levels.
Filtered coffee does not have the same effect as the filter catches the oils and these diterpenes. So filtered coffee would be much better for you.
Better than that would be trying green tea, green tea whilst having more of a gentle stimulating effect than coffe also contains catechins which are potent antioxidants.
I do know quite a bit more about caffeine and xanthines and the effects and processing methods so can offer a bit more info if needed.