Honestly, it's right there in the names. Helvetica projects a very Swiss Modern feel to it. Sometimes that's what you want, sometimes it's not. Univers is the most neutral typeface around that's got any personality at all. (I've always felt Haas Unica and many of the modern sans faces, especially the "brand" ones, have so little character to them that they're just completely bland and uninteresting.) Univers just... is. It's Frutiger's best design, and that's saying something.
Other favorites of mine include Trade Gothic (& friends) and Futura. I'm a huge fan of the 1930s-1970s "industrial" look, like you might find stamped on motor nameplates for heavy machinery, or the Apollo cockpits, or the IBM 360 consoles. These designs just scream _solid_ in a way that modern stuff... doesn't. (Maybe because it isn't.)
(Tangent to a tangent: does anyone know what typeface HP used on their equipment in the '70s through '90s? It's a very close cousin to Univers, but not identical. Maybe something internal only? I don't think it's just an odd cut of any of the usual suspects either. This is another typeface that has always connoted reliability and stuff that Just Works to me.)
Still, though, like you, I'd say Univers is my favorite more days than not. If I had to pick only one typeface, it'd be the one (more days than not)... just don't make me do that :)