At
http://www.avonracing.com you can download the data about avon F3 and F3000 tyres used few years ago.
I downloaded them long ago so I don’t remember the data exactly, should look in the other computer, but IIRC for F3000 the peak of (lateral force / vertical force) was at about 1.7-1.8.
BTW, the peak, and the slip angle at which the peak is located do change with vertical force, and other parameters.
Just take a look these are very interesting data.
As for soft vs hard, certainly I don’t think there’s a huge difference, in F1, between the two different tyre compounds available in term of maximum grip, I wouldn’t even call the two specifications soft and hard, most of times are two different tyres, not only in term of compound but also of construction, designed to work in different conditions.
Qualifying tyres used for example in motogp are a totally different matter, these guarantee an enhanced grip good for at least 1 sec per lap, roughly 1% improvement on laptime, but I don’t know how much it corresponds in term of maximum grip.