Hi Mark, I'll be happy to help you with this!
The i5-6200u should have four THREADS, but only two CORES, which would make it a dual-core processor.
Are you sure wherever you got that info is listing the CPU as a quad-core processor?
Thanks, ***** ***** do see on that page that it says the i5-6200u is a quad-core processor, but that's actually not accurate. Here's Intel's spec sheet on that particular processor:
You'll see that it only has two cores.
Regarding your question on performance, here's a performance chart that compares the i7-6500u with the i5-6200u and the i5-5200u:
As you can see, the i7 edges out the i5 in all tests, though the performance difference in negligible. In the real world, you probably wouldn't be able to notice the difference.
Let me know what other questions on your have on this and please remember to rate the answer for me.