I wondered how these things work out in practice, as the difficulty of adhering to a diet or exercise plan is a real factor

I found this https://pmc.ncbi.nlm.nih.gov/articles/PMC3339766/

TL;DR; in that study of 4k people:

"A substantial proportion of obese U.S. adults who attempted to lose weight reported weight loss, at least in the short term. Obese adults were more likely to report achieving meaningful weight loss if they ate less fat, exercised more, used prescription weight loss medications, or participated in commercial weight loss programs."

Also somewhat interesting that eating diet products negatively correlated with weight loss

One could read that as exercising more or eating less both work.