TL;DR: A Venetian cutaway is rounded, a Florentine cutaway is sharp. As a mneumonic, you can remember that the Florentine is like floss, which feels sharp on your gums.
A Tale of Two Cutaways
The cutaway of an acoustic guitar gives access to the upper frets. The luthier provides this access by removing part of the body of the guitar under the upper neck. The luthier may choose to shape the cut-out a few different ways. The two main variations are Venetian and Florentine.
Venetian cutaways are smooth and rounded, and much more common in contemporary acoustics.
Florentine cutaways are sharp and are terminated in a point of some sort. These are less common.
The terms appear to have nothing to do with Italian geography. Instead, guitar makers brought them into usage in the first half of the 20th century.
Some folks claim to hear a tonal difference in guitars with differing styles of cutaways. Most folks, though, agree that the cutaway style does not affect the tone. It is primarily an aesthetic device.
There’s lots of forums out there debating the merits – aesthetic or otherwise – of these cutaways. You can check out a few here, here, and here.
As for me?
Personally, I’m not the most delicate player. So I prefer less sharp edges, simply so I have less opportunity to bang it on something. Not very sophisticated, I know. But practical.
I agree with your final comment; if it’s sharp, I will, ultimately, poke myself (& others) with it. I have an abundance of scars on my hands as living proof.