More info, please. From your post count, I realize you are not a novice and have a particular purpose and matching rifle in mind.
My thoughts; What scopes and what are the intended use(s)? How much weight and bulk do you want to carry around on top of your rifle? How often will you use it at high magnification, or in low light? How close up will you need the scope to focus? What field of view will you need? Those would be my primary questions, everything else being equal. One other question would be whether you can use your existing mount, or might have to buy a higher one for the 56mm objective. Other questions will be whether you will be using a sunshade with the high powered one, and what overall length will be as mounted and whether it will interfere with your front sight, even a folded one.
Just for illustration: First photo below is my carbine with the 6-24x50mm Burris Black Diamond/Pentax target scope installed with its sunshade. High magnification scopes really benefit from the sunshade. I'll not go into the technical details here beyond sun flare and mirage at high magnification.. Note that I had to use an extra high 1.93" LaRue SPR QD mount to get it high enough to just barely clear the front sight with the shade in place.. That is with a 50mm objective lens. 56 will be even worse. Below it in the second photo, for comparison, is the more normal sized 3-9x in the standard height mount. That is likely to be similar to the 3-15x50 you are considering, although a larger objective on the one you are considering.
I do not use that 6-24x50 scope except for load development and certain target shooting or long range shooting because of its size and bulk. Those tasks take up only a very small percentage of how I use the rifle. It is superb for those limited purposes. Normally I run the 3-9x40mm tactical scope in the lower LaRue QD mounts., or a red dot, also QD mounted. The 3-9x It is far shorter, lighter, and makes the rifle much easier to handle compared to the big one.. High magnification scope sure have there benefits when precision is needed, but it does come at a considerable sacrifice in bulk, weight and handling. I don't have the dimensions of the 5-22x56 you are considering, but it is probably similar to my 6-24x50, and certainly has a larger objective.
Just something to chew on when making the decision.