Imho for start better binance. Bittrex is full of old coins forgotten buy their devs now. They are delisting lots of them now. Most of new coins adding on binance first.
Bittrex were delisting coins to improve their services, both exchange binance and bittrex have a much secured system, it will just depend on what can we will gonna trade but as much as possible if your coin is present on any of that exchange ,better used them.