Dear Max,

You will have to check your sequence parameters to verify but most probably the 2D/3D difference is in fact the reason for this.

In 2D sequences only one slice is excited at a time, which requires a certain slice thickness to provide sufficient SNR for your image. In a 3D sequence you preserve high SNR by always exciting the whole slab and performing a three-dimensional FFT. This allows for higher and especially isotropic resolution (but usually also requires longer acquisition time because tricks like interleaved acquisition cannot be performed).
If you want to have the same image quality in all 3 dimensions, you need to acquire your images with isotropic resolution. Your 2D sequence will most probably have a slice thickness that is much larger than the in-plane voxel size. Additonally, the slices may even have been acquired with a distance between them (parameter Distance Factor) to reduce influences between them.

Hope that helps,
Bernhard