How does the iPhone 5s compare to the S4 and Note III?

Speed and performance wise?

Added (1). I'm aware they are different operating systems.

You are talking about two completely different operating systems. However, the S4 has more features and power than the iPhone, and the Note III(although not yet released) is expected to blow the S4 away in features.

Both are good but i think iphone5s better then samsung galaxy s4!

Don't think there are any benchmark scores for the Note 3 (not III) as of now but the 5s "mutilates" the S4 on those benchmarks.

http://www.anandtech.com/show/7335/the-iphone-5s-review
See here.

This is good question and one that we hear a lot with our customers. I'd like to try and help you if I could.

First of all, whilst I really want to help you, I would recommend that you read around on the features of the 3 handsets that you have mentioned. We always tell our customers to try and gain info from multiple sources to ensure they get a balanced view.
You have mentioned 3 great handsets here, all of which are quite different but great in their own right.
It is difficult to determine which is faster at the moment as we haven't been able to conduct any benchmark testing. However with the iPhone 5s Apple have not only used the new A7 chip which brings 64bit technology (the first of its kind on the market) meaning up to 2x faster performance. They have also introduced a new secondary chip, called the M7 Motion Coprocessor. This means that motion tasks are handled by the M7 to preserve the battery life.It's all very clever.
The Galaxy S4, as you know is the latest and greatest smartphone offering from Samsung, from a speed and performance point of view the 1.9 GHz Quad Core processor is right up there with the best available at the moment. It means it's going to be difficult for current Android handsets to compete in the speed stakes. Why not take a look at a review video on our blog - http://www.dialaphone.co.uk/blog/2013/04/25/samsung-galaxy-s4-review-samsungs-tour-de-four-ce/ for info information about its features and performance.
The Note 3 is due for release this coming Friday, so reviews are a little thin on the ground at the moment, we do have a first look on the blog at the moment which will offer an overall, I'm sure we will have full review in due course. From a specs point of view it does have a beefier processor than the S4 with a 2.3 GHz quad core, but then it does have a host of extra features and that huge 5.7" Screen.
In Summary, each handset that you have mentioned here is arguably the best in its particular field, but which is best for you should be determined on how you use a phone and which features you find to be most useful.

I hope this helps you out, have fun in your search.