I have one of each. I like the stick, but I reluctantly concede that the control wheel has some benefits, depending upon the control forces. Pitch is not really an issue, but roll can be.
If the aileron forces are light, a stick is crisp and a delight, and control wheel not really beneficial. But, if aileron forces are high, the stick can be very unpleasant in gusty turbulence. My Teal is stick, and has very heavy ailerons. They are so, as they are designed so you can pick a heavy wing out of the water at low speed, and this works. However, it makes all the rest of the flying not so nice, a lot of muscle required, in an awkward direction for your arm. The Lake amphibian is extremely similar to the Teal in regard of ailerons (same designer, same operating environment). The Lake, however has a control wheel instead of a stick. You don't notice the heavy roll control.
It can be noticed when the forces required for flight in turbulence are not harmonized between roll and pitch - much more roll force required than pitch in some cases. This can lead to PIO, if you are applying control by feel, when the feel in roll is quite different than in pitch.
However, when planing on the water, precise pitch and roll attitude is important, and in this condition, the controls are nicely harmonized, though you're not displacing them much. you can "stir the pot" and the plane follows nicely, about like a helicopter - quick and precise. This is not so easy in the Lake, and not as natural.
I opine that that the feeling of "heavy" in roll with a stick is because to move the stick in roll, your arm has only one motion, which is not really a normal one, unless you're very used to plying through dense brush a lot. Whereas, with the control wheel, you have a lifting motion of your arm, combined with a rolling motion of your wrist, where you do have a fair amount of strength. You can get greater leverage with a control wheel. Indeed, when I was trained on the DC-3, it was specifically pointed out that the control wheel goes all the way around - right upside down, through to right upside down. You have to remind yourself that this amount of control is available, 'cause it's not natural! I suppose that Douglas back in the day used this to maximize control effort verses effect.
The AS350 helicopter is very light, with hydraulic controls. You quickly learn to rest your wrist on your leg, and use only a thumb and forefinger to fly, or over control is certain. However, the MD500, with manual controls requires muscle. but offers amazing natural feel while flying.
I suppose the the control wheel suggests that you can get both hands on it, to get full control in difficult circumstances. I have a few times had to do this, and certainly would not be here if the plane had a stick. While right seat PNF in a Piper Cheyenne, and just airborne (night, heavy snow, northern Ontario runway) the PF said "help me fly". What?! 'Turns out that we had one empty tip tank, and one full one - 400 pound fuel imbalance at the tip - fueling error. Yup, we needed the leverage of the control wheel.
So, it depends upon the aircraft type and nature of flying, each arrangement has it's merit, as long as it's designed in where it is needed.