Obviously, "less productive" is an implicit comparison with some base level of productivity, and we don't know what that level of productivity is. I think that the author implies that he thinks his base level of productivity is "high enough." On the other hand, reading between the lines, his coworkers may think that his base level of productivity is "not actually all that high." And we don't know how much less "less" is.

If an employer has a choice between "happy, unproductive employee" and "unhappy, productive employee," I'll suggest that the rational approach is to get "unhappy, productive employee." In that scenario, you'll get useful work out of the person until they quit, and then you'll have another chance to hire someone who's happy and productive. In the happy, unproductive scenario, that person is a drain on your resources until you fire them, which is inherently more expensive than someone quitting, and often more of a morale hit than an unhappy person quitting is.

(Any real scenario will be more complex than the previous paragraph).