As with everything in aviation, there's never one simple answer. As explained above, the minimum approach speed is a mandated number, based upon the stall speed. As the stall speed varies with configuration and weight, that number will be higher with less flap or more flap.
But, another part of the equation is that the approach speed chosen should be 'speed stable'. The total drag graph for an aircraft is an inverted bell shape. All other things being equal (hah!), the approach speed should be just above the min drag speed. The reason is that if the aircraft is disturbed (and no approach is ever totally stable), any increase, or DECREASE, in speed will result in the drag changing in such a way that the aircraft will tend to go back to its original speed without pilot intervention. Faster, more drag, so it slows again...but slower, less drag, so it accelerates.
If you were to choose a slightly slower speed, right on min drag, the speed would only be stable in one direction. Faster, more drag, and it would slow. But, slower, also more drag, and the deceleration would continue.
Conversely, if you choose a speed lower than min drag, the speed becomes unstable in both directions. Some military aircraft are operated in this area...generally carrier based aircraft, where the most important factor becomes the final energy at touchdown, and ease of flying, or safety, are secondary.
So, are the bigger aircraft approach speeds higher than the smaller aircraft? In some cases, but it has much more to do with wing loading, and wing design. Wing shapes that work well in the cruise or high speed parts of flight, mostly aren't nicely behaved when slower. A reasonable way to guess relative approach speeds is to look at wing area vs weight. This is called wing loading, and is measured in pounds per square foot. The lower the number the better. Again, with the rule that there is no free lunch in aviation, a nice low wing loading, that gives low approach speeds and low stall speeds, will also be more affected by any gusts...i.e. it won't be as nice a wing in turbulence.