This is a simple one that works for me:
Most custom type plugins use standard WP functions, and work just fine. If you’re not sure, ask the author of that plugin if there are any limitations when importing data.
The ones I’ve seen that are incompatible have issues when importing ‘enhanced’ field types – not something as simple as a custom post type.
I haven’t tried ECPT or Types & Views, so they may well work just fine. I just mentioned the possibility of incompatibility because no details were given about the error.