I doubt any Watch apps are remotely taxing to any recent iPhone, but I could be wrong? I also suspect that whatever speed increase the 6 has over 5 will be mooted by the lag in BT transmission.
I think where the differences would really come into play would be between versions of iOS. I'm sure there are versions of it which will not play nice with the Watch compared with others.
It stands to reason that any apps that have a component running on the iPhone, that the 6 will perform better than the 5. More powerful CPU, more memory.
Whether it's noticeable or not is going to depend on the app.