Although I have a Pedersoli Kodiak Express with .58 and .50 barrels (swapable) and Kodiak Safari Express is in .72 cal I chose to reply, because when I was considering which Kodiak to buy I did a lot of online research. Please note the kind of loads I'm talking about below far exceed Pedersoli recommendations. If you choose to use them you do so at your own risk. However, I noticed that Pedersoli is often over conservative with many load recommendations. For example in a 58 cal howdah pistol they recommend a max of 35 grains of powder when it uses the same barrels (but shorter) as their 58 cal kodiak rated for 110 grains. I found the howdah works best with 50-60 grains.
Coming back to the subject personally I would consider Kodiak Safari Express for hunting only if all your hunting is done at distances up to 60-70m at the very most (50 comfortably). Kodiak Safari Express with its .72 cal 1:75 inch rifling twist is a patched round ball rifle and a patched round ball looses its speed very quickly. Even if you load is pretty hot with 150 grains of powder and you get 1450 fps from a 500 grain patched round ball giving you 2300 ft-lbf of energy, in 30 meters it looses 20% of it. Don't get me wrong. Even the 1100 ft-lbf is enough to humanly dispatch the biggest American or European game in many countries there are muzzle energy limits. For example here in Poland to hunt Elk your gun has to have 2500J or 1843 ft-lbf at 100m from muzzle. So depending on where you are this may be a non issue for you.
Accuracy-wise I would expect a well regulated load to shoot 2 inch per barrel 5 shot groups at 50m, and shots from both barrels to be in the same 6 inch circle (many rifles are better than this - occasionally I read about a worse one). My .58 is pretty much like this with patched round ball. My 12 gauge smoothbore shotgun puts all shots on paper at 50m with a 72 ball - The paper is around 12x12 inches. I'll leave it at that
If you're planning to load it sufficiently hot for proper "express" velocities (so 1400-1600 ft/s) expect a pretty stout recoil (50 to 60 ft-lbf). For hunting this is probably acceptable, but bear in mind you'll have to develop the load for the rifle at the range. Also, it is very important during your load development you shoot the rifle off hand (the best) or standing with your hand resting on a shooting sticks and the rifle on that hand being held as if you were shooting off hand as the point of impact will be different when shooting from a bench rest. If you;re not going to load it to express speeds but you'll stay in the 1050-1200 fp/s range the recoil is less noticeable, but you'll have slightly worse trajectory. If you set your sights to 50m, the ball will end up 3 inches lower at 80m, if this is acceptable to you fine, but then what is the fun of having a big bore express rifle if you don't load it to express velocities
So if the above matches your requirements I would go ahead and buy it if I was you. However, personally I bought a Kodiak Express with 58 cal 24 inch barrels and another 28 inch .50 cal replacement barrels because when shooting 270 grain round ball with 120 grains of powder I get 1650 fps so I get the benefit of the express velocity while the recoil is much less. (I also wanted a pistol grip). I have an option to put a 450 grain conical (Lee REAL) in the 58 cal and it is actually even more accurate than with round ball giving me comparable energy to similar weight .72 cal round ball in Safari Express while being more flexible. I also have an option of a long 500 grain conical loaded hot in the .50 cal barrels for shooting at over 200m (no such requirement for hunting here, but it is fun to have and play with) with the .50 cal barrels being much heavier so the recoil is much less, and the 50 cal 500 grain conical sent at 1600 fps still delivers 1900 ft-lbs of energy even at 200m. I also have an option of shooting short 250 grain REALs for long range plinking with negligible recoil.
One use I haven't touched upon here is hunting dangerous game in Africa. If this is what you want to use the rifle for, only the Kodiak Safari Express in .72 cal with a 900 grain conical, loaded pretty hot will meet the energy requirements for hunting for example buffalo in South Africa. The gun will do it(I don't know about the stock), but I can't imagine the kind of recoil this would generate.