I usually wear deodorant (which generally has an antiperspirant in it), but there are days when I don't/haven't; in this limited experience I've noticed I would generally smell worse if I haven't been active. It seems like being up and moving around and sweating from 'labor' rather than sitting and sweating (not sure how to word that) is less likely to significantly smell. With all that said, I do try to shower after the gym or when I return inside after working on significant outdoor projects.
P.S., another data point to consider is the individual's age, as hormone levels (generally tied to age) could also influence perspiration