Since you want to notice the difference between a sine wave and a square wave (as opposed to a sine wave and a modified sine wave), you could use a camera and a lightbulb for this.
For this, you need to setup your camera and environment in such a way that you can make 2 pixtures from the same lightbulb, connected first to your normal power outlet, and then to the power outlet of the UPS
If your camera has a manual expose mode, you can use this, and the lightning output of the bulb connected to the normal household power should be significantly weaker.
If your camera has no manual expose mode (most phones), open the resulting pictures, and see if the lighting time is significantly different
This difference is lighting output is caused by the fact that lightbulbs use the average voltage, while the UPS with it's square wave is designed to match the peak to peak voltage of a normal outlet, as most advanced electronic devices use diodes to rectify the power