When it's fresh the flavor is pretty close but of course the texture is different. I'd imagine pre-boiled with salt and vinegar it'd be stable longer. It tastes fresher and more potent to me than onion powder or dried minced onion which is more what I'd replace with it.
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.
