What advantage does worm tea or compost tea have over urine?

Both compost tea and worm tea need extra infrastructure to collect or extra time to brew. I make more urine than I can come up with uses for.

Why would I want to put in the effort to get worm tea if I can use urine for fertilizing, foliar feed and to water my compost with?

Urine, as it comes from the source, is sterile. If it's not, that means you have a bladder infection. It's pretty much pure nitrogen fertilizer that has no beneficial microbes with it. Worm tea and compost tea are teeming with beneficial microbes, ready to compete with plant pathogens that are trying to get a toehold on your prize vegetables. If you douse your plant with fresh urine (properly diluted, of course), that's going to give the plant a nitrogen boost, but then it is still on its own to fight off microbial nasties that might be lurking. If you add your urine to worm or compost tea, then you have provided lots of good bacteria and other microbes that can squeeze out the pathogens.

What John said.

Tea=probiotics. You don't need to get too fancy with your brewer, just getting it to be a starter culture is a huge benefit and that only takes an hour or two.

Darrin Doherty talked about not even brewing tea, just applying molasses to feed the microbes already in the soil.