It's not really a versus thing - food hardly ever is. But given that frying fat is generally a good thing (not for health, but for deliciousness), what do folks do in terms of frying cheese?
I buy queso frier and just cut into fingers and throw into my deep fat fryer. Take out when the skin is brown and crisp, and serve with a nice smooth, spicy mexican salsa (the cheese is bland and really needs the spice).
Here's someone making what's called a chupaqueso from what looks like a grated cheddar/jack mix. This is new to me (not that I haven't "accidentally" pan fried cheese when making everything from grilled cheese to a quesadilla). I have no idea how authentic this is in terms of Mexican, or any of the variants.