Watch the Root Down online guitar lesson by Fareed Haque from Soul Jazz Survival Guide
Generally speaking, I find that using the more complicated approach builds tension and using a less complicated approach builds groove. If you only have groove, it can be snoring boring. Only have tension, it's also snore boring. Using them both to create drama is musicianship.
If you really want to get an idea about how jazz works, check out the great comedians. They get timing better than anyone. In music, if the timing is off, you might be called brilliant or intellectual or abstract or modern. In comedy, if the timing is off, you're just not funny. No one laughs. I find the best players are funny, and they have the elements of comedic timing in their playing. Eddie Harris, one of the funkiest of all time, even did comedy for a while. Great comedians are often drummers: Johnny Carson, Sid Caesar, Bill Burr, and Andy Kauffman to name a few.