Interesting perspectives from all. It just goes to show how versatile a Baritone can be, and so the perception can vary a lot from one player to the next. I think the main thing is to keep in mind what you're trying to accomplish.
No doubt as friend Jon points out, you lose depth on a Baritone tuned to C. I would take exception to the description of "crappy Tenor", however. A fellow named Nick Reynolds capoed his Tenor Guitar to C tuning. Those instruments are capable of more depth than a Baritone, and yet he played it way above the depth the instrument was capable of. It just so happened that that particular sound fit perfectly into the texture of his band - some say it gave his band the unique sound that helped it reach world wide popularity. That band was the Kingston Trio, and Nick Reynolds is in the Tenor Guitar Hall of Fame as a result.
We've always felt that Ukuleles can sound nice tuned above their resonance. There is a practical limit as to how far you can go - strings will get so thin after awhile that you really can't get into the realm of the ridiculous. The trick is to keep enough tension on the instrument to give a decent response, and what that tension needs to be will vary from one instrument to the next. When a high tuning on a big instrument is well set up, it should give good volume, and compared to the same tuning on a smaller instrument, will give a sound that is less immediate, but will have more "reverb" or sustain.
To friend Patrick: at one point we likely said something to the effect that B flat was an ideal tuning, but there's a caveat. The Baritone won't give full resonance on the 4th string in it's traditional tuning. Obviously a lot of people are willing to live with that. But there is room to go below B flat and still get a fully resonant 4th string note. In A tuning, the low note is an E. A typical Baritone body resonates at D#.
When you look at how you can set up your instrument, you look at more than the instruments resonance, you look at responsive stringing as well. The deep notes of typical Baritone tuning lead to heavy stringing as well as the muffled, or "choked" note from the small body on the open 4th strings. But a year or two ago, we discovered a string formula that would allow us to go a bit lower. That resulted in our HL-SW set. It gives good tension and response in an A tuning (4th string @ E). If you're looking for a clear responsive tuning with max depth for a Baritone, then that's our recommendation. There are even people who "relax" it a step to G tuning and claim good results (@ a low tension).
As for the B flat tuning, it remains a wonderful option. Ralf mentioned capo use. It once was traditional even on the Soprano. On the Baritone, as Ralf said, it's your best friend. If you want deeper sound, but need to play in C on occasion, the capo is the answer. That's one great advantage to B flat. Ralf did his best to control himself in talking about that tuning, but if you tune your instrument to that pitch, you get a wonderful sound, and to capo to C tuning, you go behind the second fret - lots of room left on your fretboard. Medium Linear (ML) or Heavy Medium Linear (HML) sets are used for B flat tuning.
If C tuning is important, then think about how far up the fretboard you may need to go after you capo. Nick Reynolds tuned "Chicago style", like a Baritone Ukulele, and then capoed at the 5th (C tuning, like Ralf) and 7th frets (D tuning), but he was playing rhythm. Capoing from G tuning leaves you with a short fretboard. Capoing from A, or even better, B flat, leaves you with a lot more. Again, it's all in what you are trying to accomplish.
To get back to notgeorge's question on linear C tuning for a Baritone, I'm not sure if there are any options but us. We've done our best to give people a wide range of sounds and tensions there - we have three sets. wlw4 pretty much nailed the range of sounds. The LL-NW has no wound strings, the lightest tension, and the softest sound. The LL-RW has a touch more tension with a single wound 4th - it's designed to be quite a bit brighter. The newer LML-RW has a pair of wound strings. It's in between the other two as far as tone, has more tension and more power on a typical Baritone. That higher tension would also likely make it a good choice for fingerpickers like GregT.
Chacun a son gout!