In the case you mentioned, there's no real difference. As a general rule, use "on" when in doubt as it's more common and "upon" is usually for more literary or poetic uses.
Sometimes, though, you can only use one correctly. A light switch can be turned "on" but not turned "upon." Likewise, something can happen "once upon a time" but not really "once on a time."
Unfortunately, I'm not sure what the rule is here, but really, when in doubt, just use "on."