Within a script it doesn't matter which you use, but it is probably better to use my instead.

I don't want this to turn into a long discussion, and I agree that using globals/package vars for sharing data is usually not a good idea (though it does work very well for most situations where you'd otherwise use "singletons" - especially when you can Export the variables). But I don't see what lexicals have to do with the post you referenced above.
"What should it profit a man, if he should win a flame war, yet lose his cool?"

If you are using our to access data within one package only, why are you making it a global when you could trivially make it a lexical?

Here are the rules I follow. I use my unless there is a specific reason not to. I will use our for certain standard globals that need to be global, such as @EXPORT_OK. When I need to share variables across multiple files I try to use Exporter to export it from one place to all of the places that need it. If that solution won't work, then I will "use vars" for the declaration. I never use our for any variables that I've invented within my code.

I used to not use our for those standard globals. Instead I used to just initialize them before my use strict line. But it has been so long since anyone I care about has been using Perl 5.005 that I no longer worry about that.