Right, I've been running both at different points in my setup, so I can speak from experience here.
Modified sine wave (MSW) is essentially a stepped approximation of a true sine wave — think of it as a staircase rather than a smooth curve. Cheaper to manufacture, hence the lower price point. They work fine for resistive loads (heaters, lights, basic stuff), but here's where it gets problematic:
Inductive and capacitive loads — motors, microwave ovens, chargers — don't like them. You'll get audible humming, reduced efficiency, and potential damage over time. I tried a cheap 3000W MSW inverter in my narrowboat initially and the fridge compressor sounded like it was dying within weeks.
Pure sine wave (PSW) outputs an actual sine wave, indistinguishable from grid power. Every modern appliance you own was designed for this. You'll have no issues running anything.
The efficiency difference is real too. PSW typically runs 85-95% efficient compared to 70-80% for MSW, which matters when you're off-grid and every watt from your battery costs you something.
My current setup uses a Victron MultiPlus (pure sine), and it's genuinely night-and-day compared to that modified unit. Cost more upfront, but I'm not replacing damaged equipment every other year.
That said, if you're purely running resistive loads and want a cheap backup inverter, MSW has its place. But for a primary inverter in any modern home or boat? Pure sine is the only sensible choice.
What's your intended load profile? That'll probably dictate what makes sense for your situation.