Hi,
I've got no experience with Conti Sport Contact 5 so afraid I can't offer an opinion on those. However I am currently running Pilot Sport 4 having swapped from Eagle F1 Assymetric 3.
The Goodyears are a great tyre. I ran Eagle F1 Assymetric 3 for approx 35k and before that I had used two sets of the Assymetric 2 (one set on the Golf and another on my previous car). They really do everything very well. Good dry and wet grip, very stable under braking and they have a fairly soft sidewall that gives good comfort. I found the lack of noise from them was also very good. The trade-off with that slightly softer sidewall is that initial turn in to corners isn't quite as sharp as some. It's certainly not a dealbreaker though and it's only really apparent if you're pushing or drive it back to back with another tyre. They wear very well too, both sets of Eagle F1s I put on the GTI lasted me 35k or thereabouts with some rotation front to back.
This is where the Michelin Pilot Sport 4 comes in. It does everything the Goodyear does well, with the exception of maybe a little more noise. However it has a step more ultimate grip in the dry and you do get that directness on turn in that the Goodyear lacks a little. I have found it no less comfortable than the Goodyear and I am well prepared to accept a db or 2 more noise to get the increase in grip that the Michelin brings. Time will tell if it wears as well as the Goodyear, I have only had the Michelins fitted for 3k so far.
Basically I wouldn't hesitate to recommend either the Goodyear or the Michelin. You just have to decide whether you think the Michelin is worth the extra. For me it is worth it, to know that I have the best tyre possible, provided I can get the same sort of wear out of them, I'll be sticking to Michelin's come tyre change next time.