More & Bigger
I've seen the comment before about how flyfishing doesn't produce more fish, but it's not what my experience has shown.
Think about this: What do you fish with a spinning rod? Jigs, plastics, lures of all kinds generally imitating minnows, and various baits. Now that's a light summary, but you get the idea. What makes up the average trout's diet? Well, it depends largely on type of water, seasonality, and all kinds of factors but worms and minnows are a very small percentage. The vast majority of the diet consists of the various lifecycle stages of chironomids, caddis, mayflies, scuds, sowbugs, leeches, and so forth.
Minnows and the like are often targets of opportunity, hence the rather universal usefulness of standard lures. Fish can be persuaded to go for the big meal at times. Other times they are very, very selective and will take only the size, color, and pattern of organism which they are keying on. Fly fishing gives you access to this vast world of specialization, targeting the fish with what the fish are taking on that day, at that hour, in that minute. It's not too different than your own appetites. Sure, a big fat lure like a hamburger will get your attention sometimes, but it won't if you're in the mood for a piece of apple pie instead.
I have consistently caught more and bigger fish on flies after the learning phase of fly fishing -- which takes some dedication. Spin fisherman often give looks of total disbelief when you tell them you caught 20, 30, 40, or 50 fish in a half day, thinking it to be some sort of gross misrepresentation of the facts as they are used to a great day meaning a limit of 4 or 8 trout with perhaps a handful of released fish. Flyfisherman who are on their game generally AVERAGE between 20 to 30 fish per half day, with the other numbers I mentioned being common enough to experience every season. If your averages are less, consider switching. If they are more, you're a better spin fisherman than I am!