First, you must start to appreciate that there is a difference between a CONCEPTUAL model and a LOGICAL one.
CONCEPTUAL models can be drawn in the form of an ERD, UML class diagram, or various other modeling/drawing techniques. Such models are almost always incomplete, and that's deliberate, as such models are used for the specific purpose of highlighting only certain aspects of a system.
LOGICAL models are the complete enumeration of :
(a) the full logical structure of all the tables in your database, PLUS
(b) a formal definition of all the constraints that govern this logical data structure.
"full logical structure" includes : name of the table, plus all the attribute definitions (name + data type).
"all the constraints" includes : the key constraints on the tables, the foreign key constraints between tables, PLUS all the other business rules that do apply to the model, but do not fit the first two categories.
Logical models as per this definition are hardly ever spelled out anywhere, so I think I'm safe assuming that you are actually not really talking of LOGICAL models, but CONCEPTUAL models instead.
And there the answer is : include or exclude stuff depending on what exactly the message is that you want to convey to your audience. If that includes data types of the attributes, then include the data types. If it doesn't, leave them out. If a certain table has no role to play in the story you want to tell the audience, leave it out (and of course also its relationships). If relationship cardinalities are important in your story/for your audience, include them. Otherwise, leave them out. etc. etc. etc.