Is anyone aware of a way to copy field values from one feature class to a field in another feature class either python or modelbuilder?
With a common attribute (single field) and a one-to-one or many-to-one relationship between target and source tables you can use a join and the Field Calculator. Just make sure you use the Make Feature Layer tool in ModelBuilder before attempting to join a feature class or table to another.
If the relationship is only spatial then a Spatial Join may be needed in addition to the join and field calculator.
More complex relationships based on multi-field relates would require Python and cursors. So more info about what the relationship is between the source and target feature classes/tables is needed to know what you need to do.