Which is better 60 amp converter or 1000 watt inverter

Assuming your trailer currently has neither...I would go with the Converter (RV name for battery charger). Otherwise, once your battery is drained, you are completely out of electricity (I'm presuming no other charging source and not hooked up to shore power)

Of course, in real life it's apples vs clydesdales...they are two completely different things...other than clydesdales like to eat apples.