These are great instruments, and can be used for lot's of different situations. I have a Danelectro Baritone ,and pull it out all the time,especially for Country tunes, 50's stuff and anything that needs some twangy snarl. The Dano came tuned "B" to "B" but I normally use a heavier set and tune "E" to "E" in the same range as the Bass guitar. While I certainly don't play it everyday, it's a cool tool to have in your arsenal. I tend to use it when I'm not the only guitar player in a group.
Lot's of older stuff from the 50's and 60's feature Bari's. They would use em in the studio back when Upright Bass (or even Tuba's in some cases!!!) was the standard. They would overdub Baritone or "tic tac" bass to shadow the upright Bass to make the low end stand out more on small radio speakers and transistor radios.
If your looking to play professionally, you'll eventually find yourself being called to play a gig where these old tunes fill the setlist. Get yer'self an inexpensive Baritone, and bring it to the gig.....you'll be a friggin hero and get called for more work in the future!!!!
Ian