Ok, given that it's about an individual, but purely professional, I think you need to be honest but positive about it. Honest, because if the same problem will exist with your new boss, everyone needs to consider that. But positive because it's never a good idea to have a whinge about your current boss at an interview.
You know that both of these questions are likely to come up, so think very hard about the answer and be very ready.
If you say "Although the projects are interesting at my current work, I am looking for new challenges and opportunity to grow. I believe that your company will offer me to grow," then you're going to have a hell of a problem when you say that your boss may hold a grudge and may not give you a good reference.
And, make no mistake, you are going to have to say that. Most candidates can get good references from previous bosses. If you can't then you need a good reason and an alternative.
So make the answer to the first question a mild preparation for the second question. Make it clear that you have no ill-feeling and you think that, in most respects, you think your boss is a decent guy and a decent manager. Then go on to explain that there was a disagreement. Be as specific as you can be, but obviously avoid mentioning if it turned into a physical fight or something.
Then turn it back to a positive note. Make it that you really think it's better for everyone -- you, your boss, your old employer, and your potential new employer -- that you make a new start somewhere else, where your skills are respected and your past and future are positive.
Again, sandwich the negative in two positives and keep the negative as brief as possible, most people won't even notice it. But they will be prepared when you come to talk about references.
Then you can be quick to say "I really don't know if my boss is holding enough of a grudge to withhold my reference. I will ask him, I don't think it will be a problem, but if he is unwilling, would you accept a reference from ..." [be very prepared with a name and title]
Also, don't be afraid to approach your current HR about a reference. HR will be very wary of allowing someone to say something bad about an employee while representing the company (particularly if it's a written reference). That kind of thing can land them in court and it's not a risk worth taking, when the perceived "problem" is leaving them.