I used to pedal a lot slower than I do these days. I'm not sure I got a benefit speed-wise, but I can readily feel what is optimal - if I shift to a higher gear but keep the speed the same, my legs start screaming at me after a while (this is when I am going fast). If I shift to a lower gear my legs spin like mad but don't get tired, instead my lungs start abusing me.

Every person has an optimum cadence where they will feel most comfortable. As you get more experienced, that cadence tends to move up a bit. No need to artificially start riding at an uncomfortable cadence. You can from time to time just to cadence training drills, spin as fast as you can without bouncing on the saddle. This will smoothen your pedalling style tremendously.

My legs used to be stiff all day at work after commuting but it has been a long time since I had that. I am not sure if that is due to higher cadence (and therefore lower stress on the muscles) or simply the legs are stronger.