Why does this AC-DC converter have Live and Neutral inputs specified?
I would guess that there is a fuse or other kind of overload protection on the input, and for safety reasons you would want that to be on the line input. The neutral connection, at least in the U.S., is connected to ground at the breaker box, so the line connection is the more dangerous of the two. If something goes wrong, you would like to isolate as much of the power supply circuitry as possible from the high-voltage line input and not worry as much about the neutral input.

So, it doesn't matter electrically but the power supply might be a bit safer to use if you connect line and neutral as they are marked.