Performance of an engine/prop combination also depends somewhat on the aircaft, engine tuning and pilot skill...

The 10X6 to 11X5:::
Should see a lower top airspeed with the 11X5, unless the plane's drag prevented you seeing the extra speed the higher pitch prop SHOULD give.
You will see slightly faster accelleration on the ground, and better climb with the lower pitch prop, unless the aircraft has better than 1:1 power:weight.
You will be able to slow down for landings better with the lower pitch. (very important on light slow flying planes, especially 4*40 and most trainers)
The longer lower pitch prop will also help prevent overspeed in a dive. (nothing prevents overspeed if diving with full throttle)

case in point that airframe matters... my Fokker Dr1 flies faster with a 14X4 than with a 13X6... needs the extra pull at low speeds from the longer prop. Same max engine RPM both props.