My feeling is that you do either, depending on the day, and both over time. Doing full weight builds strength; doing full intesity improves metabolic conditioning. In crossfit, you want both. Mix it up, but know that some WODs have everybody resting multiple times.
In your example, where you can do most of the specified reps, I'd suggest going full bore and resting as you must. I'd say the same if you could do 10 pullups. If you could only do five and might take 7 subsets to get in your first set of 20, it would make more sense to use an assist, so you don't stand around with worked arms getting little metabolic conditioning benefit. For something as fundamental as pullups, however, it could also be worthwhile once in a while to do those 7 subsets of 2-5 pullups, just to build your pullup strength. You can always add a band for your second set of 20, just to keep things from getting silly.