Groan. I would say questions about Metz v Avon Cobra v Bridgestone Exedra Max have been answered at least a dozen times in the last 12 months alone. There are more threads about this than anything else on this site and the answers are still exactly same. I must be bored or something and this is going to take me longer to type than it would to search but here goes.
I'm talking here based on
my experience over 70,000km and referring only 240 size rear and 150/80-17 front.
If anyone disagrees, tough sh#t, it's my opinion.
Metz rear is only just OK when it's brand new. Grip is quite good but after about 2-3,000km it starts to go off. Mileage sucks. If you ride hard expect about 5,000km but the handling will be atrocious for at least the last 2,000 of that. Some nancies seem to be getting close to 20,000km but I can't imagine how you'd do that. They're obviously riding the wrong bike. The front will last slightly longer than the rear but its handling sucks even more.
Avon rear has great grip and handling in the dry but is skittish in the wet, especially on acceleration and braking. Expect about 50% more out of one (front and rear) over a Metz and handling doesn't go off until you get down near the end. The front Avon is the best I've tried (out of Metz, Avon and B'Stone). I'm on about my 6th or 7th front and still yet to have a "moment" or loose confidence with one.
Bridgestone Exedra Max (not the Exedra) is easily the best rear by a huge margin in every respect. The higher profile is also all positive, even down to correcting your speedo. Expect double mileage over a Metz although handling will start to go off a little when about 75% worn (ie about the full life expectancy of an Avon) and get progressively worse - but only a little still a lot better than the others right to the end. Front (only available in an Exedra - not a Max) gives good grip, is perhaps the best in the wet when new but only lasts a fraction as long as the Avon. It looks awful too. If you don't mind replacing front tyres every 2-3,000 km it's a reasonable option.
I've heard good things about Dunlop front and would be wary of trying a Shinko, although I've not tried either.
Some people have gone for smaller sizes on the front - notably Michelin Commander II in a 140 and Bridestone Exedra Max in a 130. Both seem to do well if you're into trying a different size.