L298N vs Motor Shield R3
Yes.  The shield is easier to user, but the breakout board you've shown uses the same chip.  I'd suspect that the breakout board, which has a much bigger heat sink, can handle larger motors, though.  You'll need to put wires from PWM and digital pins to the breakout board you're showing, but it's not super challenging to use those.  I've used extremely similar boards in the past, as well as shields, and both work great.  How big are your motors?  If they're WAY too big (the breakout board can only handle 2 amps IIRC) then you'll need something else anyway.