This question is very individual.
I was a runner first, then a cyclist. I love cycling because I can eat so much more (and so many varied foods) while cycling. I can eat bars, sport beans, fig newtons on the bike. When I run, the only thing I can tolerate is gels. My stomach doesn't do well with anything on the run (or for a couple hours before that). My dh, on the other hand, can eat a full breakfast, then go out for a one or two hour run eating bars, gels, etc...w/out problems.
For the most part, calories are calories when exercising. However you can get them in to maintain nutrition is up to you and what your body can tolerate.
As far as burning calories, I burn more calories when I run than when I cycle, and most of that is based on heart rate. I cycle at about 20 bpm lower when I cycle, therefore I'm outputting less effort and burning less calories. I also can cycle for longer than I run, so it evens out in the end.

Find what works for you. Experiment with different things until you figure out what your body will tolerate (eating lots or little before runs, eating bars vs. gels when running).
Good luck!