Difference in projectors?

I'm considering swapping my small TV with a projector (for Netflix and a bit of gaming)
Now I happened upon one on Amazon (Topvision around 200 euro) that promises native Full HD and 7200 lumens.

What is the difference between these projectors and those in the price range of around 500 euro, which "only" have full HD? Is the price difference just by brand?

And are the lumens only important to have a proper picture in daylight? Can my room be darkened anyway

I look forward to answers.

Yes, many lumens are important for daylight projection.

But where is the difference to the expensive models?

In the software equipment, lens, etc.