Tweaking your technique, rather than pan choice, may help a bit - people often use whatever is to hand to make recipes, and what you have is what you have as far as pans go. I've used the same techniques on a a cast iron thaava and stainless steel griddle, and it was workable on each of them, for what it's worth.
I usually don't find using a lot of oil helpful when heating tortillas or pitas. The oily/fried crispy outside is a familiar thing, even with a cast iron pan - for some recipes made with tortillas it can be nice, but for making the tortillas themselves it's less useful. Using very little oil, or even using none at all and dry-roasting on the pan, is a better tradeoff for me - though the possibility of sticking and burning is there, and needs some work to avoid.
The oil used should be very little (if it is being used), barely brushed onto the pan, or rubbed on and off with a paper towel (one dab on a towel will last a whole batch). Sometimes, it might be easier to brush just a bit over the tortillas instead and leave the pan dry. If your recipe has oil in it, or if you just don't want the added oil, you can also just dry-roast the tortillas (and probably pitas, but I have less experience with those) - I tend to do it this way the most, since the wrong amount of oil can even encourage sticking by making the pan tacky.
If I'm dry-roasting the tortillas, I find it really helps if the surface of the tortilla is quite dry - perhaps you could lightly dust it with a bit of flour if the dough is on the moister side (and I don't even mean damp, just slightly tacky might let it catch and stick more), you want it just slightly dusty on the surface. When the pan is hot, I sort of sweep the pan with the tortilla for a few seconds at first - that is, lift the tortilla by one side and rest a half or so on the pan for a second, dragging it forward. Then, move my grip to the other side of the tortilla, and repeat.
What exactly this five second dragging-about step does I'm not quite sure, it may dry the very surface just that little bit more, it may prevent sticking while the surface of the dough is warming, but when I do this, the tortilla tends to sit loosely on the surface of the pan, and I can skitter it around with my fingers while it warms up and starts roasting. As long as I can keep it moving for those first seconds, it rarely sticks and never badly, it's always easy to pry up (or tug away from) any little areas that catch before they become problems. Half the time I keep skittering it around with my fingertips as it cooks, it doesn't seem to cause a problem in its cooking and I'm right there with nothing else to do - but once the first few seconds of cooking have dried out the surface enough so it won't stick, you can just as easily leave it alone for the few minutes cooking takes.
It also is usually only the first one or two in a batch that can get tricky, and try sticking... usually once the batch gets going the later ones don't cause problems (though I'm not sure if that's because I've worked out the variables for this batch of dough, or if the pan gets seasoned or heated to the right amount as the cooking goes on).
(I'm not sure if it actually matters, but while I have worked with tortillas, I am actually a bit more familiar with chapati... so my techniques or perspectives may be colored by that background)