Question- What's more important in a cross race- good skills or good anaerobic fitness?
Reason- good, even great fitness will only get you so far in a cross race. If you are not good at cornering at high speed or riding through mud, roots and sand you will not reap the rewards of your hard training. In order to succeed at Cyclocross you have to be efficient at getting on and getting off your bike, and know how to ride through the technical sections without wasting a lot of energy.
However, it doesn't matter how smooth you are through the technical sections of the course if you can not sustain anaerobic power for 40+ minutes. You must train your body to be able to go hard, recover, go hard, go harder and sustain that power for the rest of the race. If not, after 25 minutes of racing you will explode and the rest of your race will be extremely painful due to your body not being able to clear the lactic acid.
Remedy- One to two days a week, work solely on your skills. Cornering, mounts, dismounts and being smooth and comfortable while doing it.
On another 1-2 days a week, work on your power at threshold WITH accelerations and recovery. Then come race day, you will reap the rewards of all aspects of cross "fitness".