Which is better 60 amp converter or 1000 watt inverter

if you're replacing a converter/charger please look for a 3-stage or "smart" charger. this will help protect your coach batteries from overcharging which should extend battery life. the converter/charger does two things. it channels power from the shore power connection or generator to charge your coach batteries (and in some RVs the chassis battery(ies) as well). it also converts the 120vac shore power or genny power to 12vdc to power your lights, RV fridge and other 12v items in your RV.

you only "need" an inverter if you want to power one or more 120vac appliances such as a microwave, microwave/convection oven, TV, other entertainment devices or residential refrigerator while not plugged into shore power or running your generator. the more 120vac appliances you want to simultaneously power through the inverter will determine the size of inverter needed which in turn will help you decide how big of a battery bank you need.

You need a converter to convert 110v AC to 12v DC in order to charge your batteries and power 12v DC lights and appliances when on shore power.

You need an inverter to make 12v DC into 110v AC for running AC appliances from your battery bank.

There are combo units that do both, but can be large and expensive. If you have a working converter, and only need to add an inverter, make sure it is Pure Sine Wave output, and sized large enough to handle your projected load.

Xs and Os. You must have a converter. You might want an inverter.

Depends on what you are trying to do.
Converter changes 110v ac to 12v dc.
Inverter changes 12v dc to 110v ac.

Depends on what your situation is. More important is the charging voltage and duration. Most RVs would get on fine with less power. You may even want to limit power if the generator is small.

So post what your concerns are to consider.

Apples and oranges