Is there a formula to figure out power loss of a power inverter?
The short answer is no. 

And the long answer is that there are no general formulae that can define the power conversion efficiency of an inverter for the simple fact that design of one inverter is different to that of another. But yes, if you can ask from the vendor you bought it from it is possible you find your self an equation but that is highly unlikely.

yes, depending on the brand power loss will be different as their electronic designs are different and their lossy points are different. 

To explain more, there are just different places energy can be lost in converting from one form to another. In this case, DC power to AC power (I suppose its what your inverter does). So its not possible to come up with an equation that has a place to incorporate all different types of losses. But sure, may be your vendor may have one. 

Should you really need an idea, try measuring the voltage current of battery and  at the inverter load and performing basic calculations, you will be able to figure which brands are better and their efficiency too. But you have to be careful, these characteristics vary from one level of output power to another.