I have the Retrax and recommend it.
My Reese handle would have hit the cover when rocked over toward the side opposite the handle. First thing I did after installing the hitch was to shorten the handle a few inches. It was longer than it needed to be anyway. But I found that the hitch head bounced side to side when driving around and was annoying, so I always bungee it over toward the handle side. With it bungeed over, I probably would not have had to shorten the handle. But not sure.
Obviously your results will vary with different brand hitches.