Aerodynamically, raked wingtips and winglets provide similiar benefits--except, as noted, winglets have the additional benefit of providing a small forward vector that contributes to overall efficiency.
Both effectively increase the wing span without the penalty (tight parking) of extra long wings.
Lots of winglets are after-market modifications (easy installation, slight weight increase).
The raked wingtip is pretty much designed into the wing before manufacture, a la the 777.
I hope that helps!
[Edit: I forgot to address your specific questions. 1) The wingtip vortex is an inefficiency. If you can move it off the wing then you leave more surface available for generating lift. Both the winglet and the raked wing tip move the vortex off the wing tip *as much as possible*. This increases the efficiency of the wing. 2) Flight can be subsonic (no shock waves), trans-sonic (first evidence of shock waves), super-sonic (greater than M1.0), and hyper-sonic (greater than M3.0). A commercial airliner's cruise speed is limited by the critical Mach Number (when shock waves first develop). Therefore, most normal cruise will never see shock waves develop with or without winglets. There's just no bearing of the winglets on shockwaves (for our purposes). The important phenomenon at work is the treatment of wingtip vortices.]