Electronics (including your microwave) AND motors (refrigerators, A/C) run better on a pure sine wave inverter. "Better" means cooler as well as consuming less power.
The electronics industry has come a long way in the past 5-10 (?) when it comes to pure sine wave inverter technology. Ever since the Honda inverter generators came out other companies realized that it is not that difficult to make a pure sine wave inverter.
The reality is, a pure sine wave inverter of the same power as a modified sine wave inverter should not cost more than about $50 more. Most of the parts are the same between to two.