It depends what you're considering as earning a living. If you want to be a concert performer (soloist), it's tough on any instrument, especially piano and clarinet. Clarinet would allow you more opportunities to play in an orchestra, but it is one of the more oversubscribed orchestral instruments.
As a teacher, a pianist would have better luck going freelance, whereas a clarinettist would have to work mostly with a school/ music board. I think both instruments would be of a similar prosperity here. Much more people learn the piano, which is both a good and a bad thing in this respect.
However, there are more varied opportunities outside of orchestral work with piano... accompaniment, backgroun function/restaurant music (a summer or two on board a cruise liner doesn't sound so bad

) and the like (plus you could always turn to the pop/jazz spheres for work if you're not picky)
Both have interesting chamber music possibilities, piano duets, piano trios, accompanying groups in general v clarinet duets, woodwinds trios/quartets, wind quintets.
As for me, I've been going through a similar dilemma. Playing piano and bassoon to roughly a similar standard (piano is higher, but I've got performance diplomas in both). I know I'd have a much better chance getting a job with the bassoon (hell, I've almost been offered one with a local music centre next year), I don't think I could spend the rest of my life with it. It would be much easier to get a stable income out of, but the piano is where my true music passion lies. It is much easier to hold a piano recital than a bassoon one (let's face it, how many concert bassoon soloists are there about?

). Saying that, there are a LOT more pianists.
For me, the issue is between studying piano (with bassoon second study) or doing a more scientific (and stable, in terms of jobs) degree such as medicine. I would love to be a pianist, but the instability is the one thing that stops me from really going for it (as well as my parents

)
Pianistimo... there are probably more oboe/ clarinet concertos than you know of. How many bassoon concertos do you know? I've played 5 myself (Vivaldi, who wrote about 20, Mozart, Hummel, Weber, Jacob), including one which I was lucky enough to play with my youth orchestra (Weber). The only one that's ever really heard that much is the Mozart, but there are quite a number, and by relatively unobscure composers.