"Have you got this dress in a different color?"
"Have you this dress in a different color?"
There is no difference in meaning.
"Have you got.." is more prevalent in a conversation.
"Have you.." is more common in the UK, I believe. In the US "Do you have.." is typical.
There have been questions on "I have" versus "I have got / I've got".
I think this answer by Su Ki summarizes it very well.
(quoted from http://www.italki.com/question/337826)
"I've got" is an alternative to "I have" in the following situation only:
1..... you are talking about something which either 'belongs' to you or something which you need to do
2.....in the present simple tense
3.....in informal contexts.
For example, there is no difference at all in meaning between "I've got a problem" and "I have a problem" or between "I've got to go home" and "I have to go home". In these situations, the two forms are interchangeable.