For whatever reason, a lot of the classical musicians I know tend to have trouble with getting that swing feel. Some of it is in the bow. It complicates the problem because you have to actively think about how you're going to bow a complicated lick (I usually hook-bow swing eighths but that doesn't work all the time with lots of syncopations). In a difficult classical piece, I can look at a difficult section and mark out my bowing to keep myself on track. I really think that bowing is one of the major hurdles for an improvising jazz cello player.
I also think that a lot of jazz chord voicings are based on fourths, so being able to work around that interval is useful. When you tune in fifths you lose a lot of the standard positional tricks that you're used to and it takes a little more thought to do simple arpeggiations.
That being said, I know a cello player who is an amazing classical performer but has found a pretty hip place to sit in the groove when we play jazz. That may be because he played jazz (guitar) before he played the cello at all. I should ask him how he deals with bowing.