Can and should are two distinctly different critters. Karamojo Bell killed over one thousand elephants with a 7mm Mauser (275 Rigby). Many hunters trying to emulate Bell ended up dead. Certainly there are some who can take large game with a handgun and many do every year. But the OP is asking about two specific rifles.
The only version of the Ruger I have experience with was a heavily modified, integrally suppressed gun shooting 44 spl. Fun, reasonably accurate and very quite. A sort of modern take on the DeLisle. But at it's heart it's a pistol caliber carbine. That's the extent of my experience with the Ruger.
The CZ is a handy little rifle, but very much in the European style. The stock has a lot of drop as it's really designed for iron sights. Unless you modify the bolt handle, you end up with the scope mounted very high, which combined with the drop of the stock makes it uncomfortable, particularly for Americans who are used to much less drop and low mounted scopes.
The bolt handle mod is very simple, and allows you to mount the scope much lower. Unfortunately, low rings are harder to find because the CZ-527 uses metric dovetails. There are weaver adapters however, which simplified things.
The nominal bore of the 527 is 0.3105, and in my experience it will shoot 308 or 311 bullets equally well, although you loose velocity with 308 bullets. If you don't handload, who cares?
Early CZ carbines had trouble with the hard primers of some surplus ammo, and you could put a heavier spring into the gun to fix it.
The single set trigger seems neat at first, but unless you really like set triggers, it gets old. You can disable the set trigger, or better yet, replace the factor trigger with one from RifleBasix and get a very nice adjustable conventional trigger with a clean break and decent weight.
The CZ is all steel, with a nice finish and wood that ranges from plain to really nice.
Here's a shot of the bolt clearance on a factory gun with a Burris 4x scope. You can see how high the scope has to be mounted for clearance.
A simple mod and you can drop the scope about 1/4 inch, which doesn't seem like much but makes a big difference.
I converted my 7.62x39 carbine to a 6.5 Grendel. I should have left it in the original caliber.
Here you can see the carbine stock with its bigger drop compared to a standard 527 'American' rifle stock that I replaced it with.
Anyway, if you have any specific questions about the 527, let me know. I've owned several, just about one of every model made. They are really nice little rifles.