A sautéed onion is going to be more mellow than a raw one. The juice will be more intense per weight and volume than the minced or diced raw root. It's really a matter of a few drops for a pot of soup. In my chili I often use both yellow and white fresh onions with the meat, plus onion powder as part of my homemade chili powder, plus a few drops of onion juice in the sauce to simmer down before combining the meat and sauce.

If you're really curious, there's no description I can give that would match trying it. Just don't go crazy and add the juice of a couple whole onions to a vegetable broth. Drops really will do the trick.