Let us look at inverter efficiency.
An inverter at full load may have an efficiency of 85% and at 1/3 load 90%. This is just from memory, don't have exact specs.
So:
Eff = Pout/Pin
Eff at 1/3 load about 90%
Eff at full load about 85%
This is about a 5% difference in efficiency
Say Vdc = 12.5V, Load = 300W
Pin=Vdc*Idc
Idc = Pin/Vdc
Use 300W inverter:
Eff = 85% at 300W load
Pin = Pout/Eff
Pin = 300W / 85%
Pin = 353W
Idc = Pin/Vdc
Idc = 353W/12.5V
Idc = 28.24A
Use 1000W inverter
Eff = 90% at 300W load
Pin = Pout/Eff
Pin = 300/90%
Pin = 333W
Idc = Pin/Vdc
Idc = 333W/12.5V
Idc = 26.64A
Pdif = 353W - 333W
Pdif = 20W, 20W more from battery with the 300W inverter that the 1000W inverter.
Idif = 28.2A - 26.6A
Idif = 1.6A more with small inverter.
P = 12.5V * 1.6A
P = 20W more with small inverter!
Will be a little worse because of voltage drop as said in above post.
