I can give part of the answer hoping that some Research Gate colleague(s) to give more elaborate answer.
If a material , that will precipitate, is crystalline then the precipitation rate will be slow because crystallization is a selective operation with crystals gathering in a systematic manner & growing after which they settle down. Crystallization is usually helped by agitation, cooling, and possibly centrifuge.
If there is an amorphous "non-crystalline" material, then precipitation is expected to occur at a fast rate since it lacks selectivity.
Many materials are categorized as semi-amorphous "semi-crystalline" and these will have a rate of crystallization in between the 2 extremes "slow & fast".
Dear colleagues, I think we should be more precise. The technical term “precipitation” is a meteorological term describing the falling water either in solid or in fluid form. It is also used in some cases to describe the crystallization of minerals be it in chemical sediments or in a mineralization such as those found in ore veins. If this kind, rather call it crystallization, is the hot topic in this Q&A discussion, the rate of nucleation and the concentration of certain solubles are key. I assume that the rate of sedimentation is the topic of this question. In this case the particle size, specific gravity, grain morphology and the type of aquatic environment are the key elements of control. To give a more detailed answer needs a more precise description of the aquatic environment and its overall geological as well as morphoclimatic settings.
here I mean rate of sedimentation in aquatic sedimentary environments as a systems. When we say fast/slow rate in lagoonal basin system for example, we don't have the normal avarage of sedimentation in this environment. In addition, we should keep in our mind the differences in sedimentation rates between lithogies(evaporate, clastics, carbonate)