If an inverter has more VA (volt-amp) in unit measurement, does it consume more battery?

Ideally, the power drawn by all electrical equipment is equal to output on that. In real-world devices, losses in it are extra. Hence power consumption of inverter from battery = output load + inherent losses within UPS. For the same load, the only difference may be losses. By and large losses within the inverter is % of its capacity. Hence to that extent, larger capacity UPS may have larger absolute watt losses consumed from the battery. Incidentally ( on the other hand ) all power equipment efficiency improves with an increase in power ratings ie. larger equipment has better efficiency resulting in lower losses as % of rating. In case your two UPSs are within 1:2 power rating, mostly work in (say) 35: 85 of load capacity and not on very light load most of the time, change in loss part will not be significant and battery drainage will be almost the same. But, ensuring consequential (if any) change in charging/discharging rates of battery has no adverse long term performance or life expectancy related issues. Note: In case this is your practical difficulty, furnish ratings of two inverters & battery along with details of duty cycle( in line with / based on above details).