When making potato latkes, should I use oil or butter?

Sorry, they're just not latkes if fried in butter. They're Rösti.

Peanut Oil with a touch of Olive Oil will give them the desired crispy exterior texture while allowing the cook thoroughly.

Oil makes the best latkes especially if the potatoes have been grated coarse and drained well to get as much moisture out as possible. You latkes will fry to a rich golden color, be crisp on the outside and delicious on the inside.

So ... Why not use 50/50?
Oil is the traditional, but butter has so much to give. A mix of oil and butter will give the buttery flavor, with the flame-point of the oil. Best of both worlds

Sephardic Jews traditionally fry their latkes in olive oil because Hanukkah occurs at the end of the olive-pressing season. Olive oil was treasured in Biblical times, so using it to fry latkes gives the dish a deeper significance. Ashkenazi Jews in Eastern Europe and immigrants to America typically fried their latkes in schmaltz, or rendered poultry fat, until more healthy oil alternatives were introduced. Some cooks still splurge and use schmaltz because it tastes so darned delectable. - Shiksa in the Kitchen

The whole point of the celebration is the miracle of the oil--as in olive oil. So use extra-virgin olive oil. Anything else and they're just potato pancakes. Nothing special.

Oil.

Latkes are all about the oil

Butter burns, use oil.

My brother-in-law uses oil, so that the latkes can be pareve.