Probably the degree of formality: To me, these two are essentially interchangeable. Both are causal but correct. Have you got a pen? Do you have a pen? This one is too formal -- a little odd unless you intend to sound affected: Have you a pen? Another way to phrase the question that is correct, not overly formal, but slightly more polite would be: May I have a pen, please? Hope this helpful. I am a native English speaker from the United States, so my response might be different from a native English speaker from the United Kingdom.