If your difficult customer is often using generalized phrases ( such as your software is not user-friendly), your reply should be specific. Talk to him/her on specific areas where your product and/or services have performed extremely well. Talk about people in his group being happy about the solutions given by your own company. Be smart , precise and concise.
Be firm to oblique references
Difficult customers love to compare. You might hear something similar to these
"This product is better than yours"
"His product has X more features that yours"
"Our competitor does not use your product, why should we?"
The answer to this should be non-emotional. For e.g. let us say the question is "His product has X more features than yours". You can counteract it by saying that no one in his department will use so many features and probably he is paying for them without using them. Try your best to avoid any comparison. Say that your product stands on its merit and not on anything else.
If you feel you are right then stick to it
You might probably lose your business, if you stick to your point. If you feel that customer is let us say quoting too low a price, it is better to let him know that it is not acceptable to you. Many times, companies and vendors in the hope of getting a project in future work for a loss now. If that is your strategy fine but for longer term client will value you for how much you you helped them in resolving bottlenecks. If you decide to give in now, you will forever be asked to quote low.
If everything fails try humour.
I have tried this successfully many times but you need to be careful with it. I have used humor such as 'I think let us try with inserting thousands of records into my competitor database and see if application loads at all" or "We have the best features but I guess Mr. -- loves his budget". They really sometimes take the pressure out of the situation.
Anticipate customer's actions
If you know the things that your demanding customer puts his focus on , do them first. That would take the wind out of his domination. If you do miss out on a few things then, he wont complain.
So the rule to handle a demanding customer is
Anticipate - Gather Knowledge - Prioritize - Stay Firm