I have a 4516-1, it shoots very well, but if I had to do it over again, I would rather have the 4566 with the longer 8 shot mag grip frame.
On the 4516, the 7 shot mag base plate with the finger hold on the front, extends about 1/2" from the bottom of the frame, which gives your pinky finger something to hold onto.
But at the rear of the mag, the grip/frame is about 3/8" shorter than the bottom of the mag, so there is kind of a "gap" where your palm extends past the rear of the grip unsupported, while on the front of the grip frame, all fingers are in contact.
It may not bother other people, but I find it annoying because it doesn't give me the feeling that I have a secure hold on the weapon, plus there is less contact with the palm of your hand to distribute the felt recoil more evenly.
To me the recoil feels more pronounced and sharper with the shortened grip/frame back strap, than with the longer frame/grip of my 4506-1.
Since I do have a 4506-1, I experimented by putting the 4516-1 slide assembly on it... now that made a nice combination, that configuration is basically a 4566, but with a 3-3/4" barrel instead of the normal 4566 4 1/4" barrel.