I'm probably going with another company...
Let's stop and think. They HAVEN'T signed yet. In fact, from their response, they may not be totally sold on "the other company". They haven't signed yet, and their use of "probably" likely means they're resigned to choosing that company because it's the best the found, not necessarily THE best. So, here's how you should answer this. It's all done with questions.
1. "Hey John. Is it OK if I ask a few questions?" Invariably, unless you did a really bad pitch, they'll say yes.
2. Let's explore fit. "So, John, why did you decide to go with the other company? What was your buying criteria?"
3. Next, find out about functionality. "John, did the other company's offering include everything you needed, or were there some things missing?"
4. Then a big one - cost. "Tell me about the cost structure. How did this look? Did they give you terms, financing (whatever is applicable)?"
5. Fear. "Are there any fears or trepidation you're still having John? One's that, maybe, haven't been fully addressed. Any hesitations to signing?"
Asking these questions do 2 things. First, the will give you a huge mine of information, information with which you can start rebutting the potential sale the other company is about to get. Secondly, it helps the prospect remember any fears or misgivings they had about the other offering.
What have you got to lose? At worst they'll say no again. At best, you may actually get the sale.