I've not used the Falkens, so I couldn't comment on them.
Goodyear Eafle F1 GSD3's are a good summer tyre. Excellent grip in the dry and good progressive grip upto the limit in the wet. No nasty snap oversteer, they let you know what they're upto. I wouldn't recommend them as a winter tyre however, they need heat in them to work well and I always felt like I was on tiptoes in them when the salt went down on the roads.
I like the Toyos best having used them. Good dry grip, excellent wet weather performance and a better year round trye than the Goodyear.