How highly you are regarded in a business can have a slightly arbitrary quality.
If your present employer is 'forced' by the offer to match it, they haven't independently started suddenly thinking more highly of you - like the other mob evidently does. On the contrary, they may demand more of you to justify the extra salary.
If the other mob think you're really good, then it may also make it more personally gratifying to work for them and more opportunities may arise. If you know others who work there, ask them about what it's like.
Sounds exciting to me with the extra cash a concrete motive to take the plunge, provided the company is reasonably established and big enough. Won't hurt the CV to demonstrate a bit of independence and dash either.
