One puts out a pure sinewave, like what comes out of your wall socket at home. Very clean, you should get little or no hum from this. The bad part is that they are not very efficient (somewhere between 50-80%). Higher cost to make and buy.
The other should be called a modified square wave inverter. The waveform is a squarewave of varying duration which depends on the battery voltage. Square waves are full of harmonics and these inverters will put a lot of interferenc into your system. Their plus though is that they are very efficient at taking 12VDC and making 120VAC (can reach over 90%). Low cost to make.