There can be a small difference. In general, both expressions mean the same. But when you're in a bad situation and you're looking forward until the situation will end, you mostly use "uitkijken naar".
Example:
"Ik heb zo'n vervelende baas, ik kijk uit naar de dag dat ik niet meer hoef te werken."
In this case "Ik heb zo'n vervelende baas, ik verheug me op de dag dat ik niet meer hoef te werken." would be a bit weird, because in this situation you're not feeling excited at all.
In general I'd say "verheugen op" is also a feeling of excitement, while "uitkijken naar" can be in positive and negative situations. But it wouldn't be wrong if you'd use "verheugen op", so it's just a feeling and not a rule.