Let's be clear from the start: both tea and coffee contain caffeine. That being said, the amount of caffeine in your tea is negligible (there's three or four times less caffeine in tea than in coffee), making it a great alternative to the ever-present cup of coffee.

Also note that caffeine is absorbed differently, and more steadily, by your body when you drink a cup of brewed tea compared to a cup of coffee. This is probably why the myth of caffeine-free tea persists!

That said, the most important element in tea is theine. Now, how does this differ from what many (often wrongly) consider its "counterpart," namely caffeine?

The general consensus is that coffee is stimulating, while tea is energizing. This is why Garfield can't function until after his first cup of coffee (and he's not the only one we know of!), and it's also why people with sleep problems limit their coffee consumption to the morning, avoiding it at all costs in the evening.
In short, caffeine has an intense and immediate effect: from the first sip, your body seems to wake up all at once. The effect wears off quite abruptly after two or three hours. That's why it's not uncommon to see people gulping down cup after cup of coffee "out of necessity."

Tea and its theine, on the other hand, stimulate your body in a more subtle and steady way. You'll likely notice an invigorating effect when you drink your tea (especially if it's black tea), but this effect won't be as strong as coffee. That said, this feeling of vitality and mental stimulation will last at least six hours, enough to get you through your day with alacrity!

So, if you want to be more alert without necessarily being more agitated, tea and its caffeine content are the logical choice. Ideal for concentration and meditation.
Theine and caffeine: what is the difference between these stimulants?