It totally depends on the type of tea, the amount of leaves you use. The average tea bag contains about 2 grams (about a tablespoon) of tea. If you're making loose leaf tea, it's possible you're adding more than that, resulting in a higher caffeine content.
Tea generally has less caffeine than coffee. Black teas are generally the strongest, ranging from 20-70 mg of caffeine per 8 oz (although I have one on my shelf that contains a whopping 110 mg per serving), whereas brewed coffee generally contains 90-150 mgs of caffeine per 8 oz, though can be more if you brew it strong. Green and white teas usually have less caffeine content than blacks, almost always under 45 mg per 8 oz. Herbal and red teas are naturally caffeine free. (Mayo Clinic Caffeine Chart)
I would expect that, when switching from coffee to tea, you've been drinking more tea than you drank coffee. Tea, in my experience at least, goes down easier than coffee, and doesn't give you the same, uh, stomach issues coffee can. Drinking more would mean more caffeine, which could be the reason you're still suffering from caffeine withdrawal headaches. Switching to green or white teas could be a good compromise, just be careful to track your intake.
If you like the routine of drinking hot beverages all day and still want a bit of caffeine, you can blend black or green teas with herbals or reds to "dilute" the caffeine content. You can either do this with loose leaf tea, or making a large thermos of tea at once with two teabags (generally, use one teabag per 8-12 oz of hot water). I recommend mixing Earl Grey and lavender.