“Your competitor quoted us a lower price.”
Why they say it. They are using a competing quote as leverage, and they may genuinely see the two as interchangeable. It is often a test to see if you will fold or if your price reflects real difference.
Do not: Do not instantly match the price, which trains them that your number is fiction and starts a race to the bottom.
I believe you, and if these were identical, you should absolutely take the cheaper one, I would. The reason our number is different is the part that does not show up in the quote, what you spend less time fixing, chasing, and working around after you sign. Can we compare not just the prices but what each one actually costs you over a full year of use?
Then ask. If the cheaper option ends up needing a workaround or extra headcount to do the same job, is it still cheaper?