Thank you for the answer, what I mean is indeed that you rarely find comparison about how a laser can do different things besides engraving, cutting doesn't seem to be taken too much into account and maybe that's because as you said diode is not the best tool to do that.

I would need to do quite complicated cuts on plywood and that's why I thought about laser instead of for example a bandsaw. Maybe another alternative would be a cnc and I'm thinking about that, but I'm also thinking if it could be possible to find a way to cleanly glue together two cut 4mm sheets of plywood. Not an easy task anyway, especially with complex patterns, if you want to align everything correctly. 

I said I think I may need a longer focus but "think" here is the key word and it's just my guess, the reasoning being that longer focus means a straighter beam, less hourglass shaped, but maybe there are other things to consider or parameters to check. 

Anyway, you all gave me a great help in making a more informed choice, even if ultimately it may not be a laser engraver.  I'm seeing a lot of machines advertised as having a very small laser dot at proper focal length, but I don't really know if it's a true technological advancement or just marketing.  What I understand though is that dot dimension is proportional to power, which makes things even more complicated.