I have another rabbit question!

We have a Lionhead who is a happy house rabbit, but he is not that keen on being picked up and stroked, and never sits on the sofa with us or anything like that. He is looked after well but do you think we should get a different type of rabbit the next time, does anyone know if different breeds of rabbit are more likely to be more friendly or does this just depend on how you treat them etc?
Any ideas?? Thanks