There is simply no comparison between playing a public course versus being a member of a private club. I would say that there often are upscale public courses which are better architecturally and perhaps even as to conditioning, but they still aren't private clubs. The question is whether the benefits of membership are worth it to you and they go way behind the comparison of the courses.
There are some upscale public courses in my area which offer you an annual membership which can make it more reasonable, but when there are no tee times open, or the course is closed for an outing, or it is going to take 5 hours to play a round, the bargain is not so great.
The food minimums are usually not that steep and the prices are fair and you don't have to wait in line, etc. Many private clubs allow you to walk and carry, in fact, my home course has push carts available.
The fact is that at a private club you feel no pressure and most of the other members have the same interest as you - to enjoy the course and the amenities which the club has to offer. You want to go out and hit balls, go ahead; you want to play a few holes in the afternoon, go ahead; you want to go back out for an afternoon nine, go ahead. The flexibility is incredible.
Finally, if the club is member owned and you have an opinion, they will listen to you. It doesn't mean that the change will be made, but at least you will feel that someone will actually pay attention to what you have to say.
I joined a member owned club last year and immediately volunteered for the greens committee. You learn the economics of running a golf course and how others view golf course conditioning.
Can it be frustrating, yes, but there is a whole lot of satisifaction when you go out to your club and know the other members and there is always a friendly hello.