I think hook size is more important than hook diameter. With larger hooks, for example streamers, use barbed and not barbless hooks.
Barbless hooks penetrate deeper and larger barbless hooks can hit the brain or the carotid artery of the trout through the roof of the mouth. They also have a stiletto effect in which the move around and stick the fish multiple times in multiple places which increases the risk that a critical structure will be hit.
About Trout: The Best of Robert J. Behnke from Trout Magazine - Robert J. Behnke - Google Books
The stiletto effect and the reason that treble hooks kill fewer fish than we would expect is documented in a Robert Behnke's book, About Trout.
"There is, however a slight but consistent increase in mortality due to barb-less hooks.
John Deinstadi, a California Fish and Game Department biologist with long experience with catch-and-release fisheries, believes this is due to what he calls the ‘stiletto effect.’ Barbless hook have the tendency to penetrate more deeply. Although mortality of released trout rapidly increases with warmer water temperatures (especially as temperatures approach 70 degrees), under normal conditions, almost all mortality of trout caught on flies or artificial lures is due to rupture of the respiratory filaments of the gills or puncture of the carotid artery in the roof of the mouth. Because of their greater penetration power, barbless hooks are more prone to puncture the carotid artery. Large treble hooks often cause the least mortality because, unless the trout is quite large, the hooks cannot be engulfed into the mouth.”