I think it really depends on factors: you, your partner, your children, how long it's been since you and your ex split, if you actually intend to find a co-parent or are just enjoying dating, etc.
I have no experience iwth this, but I feel like introducing new partners as just friends is comparatively safer. Most children meet friends/acquaintances/co-workers of their parents and those people come and go. If the kids become especially attached to the person, it's difficult, but that's true no matter what your relationship to the person is. It gives your kids and your new partner a chance to get to know each other without the pressures of "Here's the person I'm considering spending the rest of my life with". If your kids are still having a hard time with the relationship ending, it also won't mean that your partner has to start out being judged against the kids' parents or automatically pushed out to avoid being hurt again. Sometimes kids will lash out against a new partner because they want their parents to get back together. Introducing a person as "This is my new partner", there are a lot of reasons that the kids will never give the person a fair chance.
I don't know if this is actually a good idea or not- it just feels safer to me.
Make sure that you know your children well. The boyfriend of my mom's who I most loathed, she thought I most liked. (I found this out after things fell apart) If things hadn't fallen apart and she decided to move in with/marry him, she would have suddenly been shocked to be dealing with a VERY difficult child. I could barely stand dinners with the man, living with him? No way.