Will either of these optics do for a 338 win mag?

[77celi]

Hey all, I recently purchased a Ruger M77 Hawkeye in 338 win mag. Currently I own a Bushnell Trophy 3-9X40 and a Nikon Prostaff 3-9X40. I have the Bushnell on my AR and the Nikon on my .30-06, but I have an extra scope laying around (centerpoint) that isnt as good of quality that I will probably just stick on my AR since it has the lowest recoil. Which of these two scopes, if either, do you think would be better to put on my new 338? The Nikon cost me a little more, but the Bushnell seems to be just as sturdy. I would prefer not to buy a new scope, but if neither of these will hold up to the recoil then I may just have to. Also, I have a 500 S&W magnum revolver that I am wanting to put a handgun scope on. Does anyone have any recommendations on an optic that could withstand the recoil but not break the bank? Thanks in advance for any help!