What is the difference between cooking homemade chili pepper hot sauce or just blending all ingredients raw?

I would say that cooked salsa has deeper, often sweeter flavor, whereas raw is brighter and fresher tasting. As Susan W has said, both are good; it just depends on what you're going for

It's a matter of preference. Raw is sharper and cooked has a smoother and more melded flavor. I prefer cooked salsas and hot sauces. There's no right or wrong. It might be fun to make both.