Oh hell, now you went and did it. The hatch covering the abyss of inverter efficiency and sine wave purity has been opened.

That discussion has been beaten to death on RV and solar living forums all over the internets. Same goes with the "choppy" nature of inverter sine waves & their effect on resistive and inductive loads.
Still... 90% efficiency sounds great but only under ideal circumstances is 10% waste "OK". By ideal conditions, I mean the entire electrical system both DC and AC being in peak condition. Other than brand new, ideal conditions are somewhat unusual in the real world. After a few mechanics and/or do it yourselfers have stuck their hands in the mix, and time & weather take their toll on a new system, things degrade to less than ideal pretty quickly.
On the topic of AC inversion for running a 3 way fridge,
IF the fridge in question is an absorption design (which is by far the most common) the principle behind the system is heat causing ammonia to convert to a gaseous state. That heat can originate from a small flame fueled by propane, or heating coils powered by either AC or DC. When the fridge is running on either electric source, there is no "start up" current spike caused by a compressor motor - therefore 175 Watts (DC) is pretty much a flat current demand whether starting up or running steady state. Setting aside start up energy, the most efficient heat source for the common 3 way fridge is propane. With little more than a pilot light flame, it generates sufficient heat for ammonia conversion to gas, at an average rate of about 1/2oz/hr. Since DC power is a precious commodity when camping, my preference is propane first, AC second (when connected to shore power) and DC as a last resort but only when batteries can be replenished by solar or generator.
In my rig, a Trace Legend II manages both battery and inversion tasks. As a battery manager, it's nearly perfect. As an occasional AC inverter, it's been super handy - but based on experience, I stay away from AC inversion tasks unless they are momentary or early in the day - which gives the solar system time to replenish batteries. If I need AC power for anything more than a few minutes, I'll run the little Honda generator, but that's just me being anal about keeping the house batteries about 11.5 V at all times.