My answer may sound a little unusual at first but think about it, perhaps it may be the way forward;
If you're talking to someone sceptical of your product .... firstly I'd suggest you try to find out why it is that they feel this way and address this. Should this fail you should consider whether or not you actually want this person as a customer or not - Stick with me on this for a moment....
If you decide that you do really want this person as a customer my suggestion would be to offer them your service for free..... Hang on, don't give up at this point, keep reading....
Let me clarify "free". Outline what it is that the client requires of your service and clarify that your service CAN meet (or exceed) their requirements .... and then provided you are confident that you can deliver as required, offer them a free trial of the service after which time if they are unhappy they can walk away with no obligation to pay. On the other hand .... if they are happy then they need to agree to purchase (and if the service is one where they pay monthly, that they also pay for the services used during the successful trial period).
I can't guarantee you'll win the business by doing this. However it'll certainly help you to identify which prospective customers are just wasting your time.
Where you are up against a competitors product, my view is that it is all about meeting the needs of the prospective customer. Most people are averse to change and need a compelling reason to do so.
If you are targeting a business customer, you'll need to provide them with a compelling business case because their drivers for change are likely to be increased functionality and/or decreased cost. The barriers you'll need to overcome can include a temporary loss of productivity, financial investment required, and that "hassle factor" which invariably has a dollar value attached.
From a marketing perspective, you need to remove the objections that are coming up for this prospect.
The biggest objection is the fear of the unknown (will I get my money's worth? will they deliver? will this guy be a nightmare to work with?). You need to make these fears go away.
How, you ask?
Give examples of your past work. Let them talk to a happy customer with a similar problem. To the extent that you can quantify your results, do. (Numbers speak louder than words. Anyone can say they deliver "cutting edge software and services," but only a few will be able to say "I saved [company] $2 million last year.")
Ideally, find someone that has used you and the competitor, and can talk to why they continue to work with you.
Also, with some products and services, you can offer a "try before you buy" version. For a services company, this might be a free 15 minute "check-up," that give them free advice, no strings, that lets them see how you think and work. For a products company, this can be a trial or review product.
Whatever you do, do not go for a competive jab. That is seen as a sign of desperation.