Regarding flaps 10 takeoff.
A small minority of pilots (Incorrectly) assume that you get a gentler takeoff experience for passengers with flaps 10 takeoff... The entire Gulfstream family climbs like crazy, especially on liftoff. It is not unheard of to find crews exceed flap 10 speed due to this acceleration, especially when flying with minimum fuel.
Takeoff comfort aside, flap retraction is usually accomplished beginning at 400', and you are climbing at 3,000 FPM, so it begins about 10 seconds after takeoff.... Flaps 20 to flaps 10 takes 5-8 seconds, but flaps 10 to flaps up that takes 20+ seconds.
The tradeoff* is 4-5 Kt increase in V1 speed, 500 Ft increase in takeoff length, and a minor second segment climb performance numbers.
Oh, if you want a gentle climb out for your Pax, just do a flex EPR takeoff, and pull the power back when airborne...
*ballpark estimates