Kawasaki, like all Japanese engines are notorious builders of strong, reliable and dependable equipment. They did have some models, equipped with phenolic cam gears that wore out prematurely...but, I think they have since rid themselves of that problem.
Kohler, also a fine engine builder, have had their problems with a relatively newer engine model, the "Courage" line. Often said "It takes Courage to buy one". They seem inherently weak and reported to break rods and/or governors long before their warranty ends. The company does stand behind their warranty and, I understand, have replaced hundreds without question. The problem remains...what do you have once the same engine is under your hood??
A few years ago, I purchase a Husqvarna with a great hydro transmission. The rider, in excellent condition, was bought AS IS because it had a Kohler Courage engine that let go at 31 hours. After reading up on forums like this one, I took the risk and bought it anyway....plus, I had a spare single cylinder, 13 HP Kohler waiting in the winds. The machine has performed flawlessly since the transplant. My wife uses it to mow 3 acres about every ten days and it still has the original blades, belts etc...here is a link to the engine swap and blown Courage: First Time Buyer & Buying Used....
You may want to take this with a grain of salt because everything I've written is only what I've heard .
Both are nice. Other than the Courage, I don't think you could go wrong with either.
I have always found the Kawi's to run a little on the smoother side than anything else, not too mention quiter. Climb aboard a machine with a liquid cooled Kawi, be that a rider or a zero-turn for example, fire it up and and you hardly feel any vibrations comming from the engine at all, they are just super super smooth running engines like Hondas. They used to always be my favorite small gas engine other than Honda in the machines when I worked at a John Deere dealer.
Personally I think the two engines you are comparing are both good, solid engines. The only experiance I have with these engines is with my tractor which has a Kohler engine and my rototiller which has a Kawisaki engine. Judging between the two I would definately put the Kawisaki a notch above the Kohler in smoothness and reliability.
However, the reliability of all engines is somewhat dependant on how well they were maintained.
I hope we are not getting you confused; like I mentioned earlier, both the Kohler and Kawisaki engines are top-quality. You mentioned not wanting to waste money on the brand name which is understandable. However, in the comparison between these engines I would be inclined to get a good one...you'll never regret it!
I too have heard bad things about the courage model - a buddy of mine got one that was a mess right from the factory - burned oil by the gallon right from day one. Their command line seems a bit better, but there are certain of those that evidently have issues with the head bolts coming loose.
Generally, I think people really like the Kawasaki's - i've had a few of them but have not faired as well as i'd like, They seem to burn through rings/valves faster than kohlers of the same age - but then I buy 20 year old machines so what can one expect?
So far, my "part-for-part" repair costs have been about the same for either line - kawi's may be a bit more.
One thing to look out for, (IMO) if you ever buy used, kawasaki tends to discontinue models more frequently than kohler or briggs in recent years. I have 4 of the Kawi FC and FV models - between 10 and 25 years old - all strong engines - all discontinued.
Now - if you want to go back to a 1972 Kohler K321 or K341 - well NOW you're talkin' engine!!
I did some additional research and found that the Kohler Courage series engines are a knockoff from the rest of the Kohler engines. For the most part, the rest of Kohlers' engines are good solid engines, but the Courage was added to the line as a cheaper alternative. I found numerous complaints about the reliability problems with the Courage engines. Not saying that it is what we call junk, but when comparing to Kawisaki it is by far the bottom choice.