Differences between a conceptual UML class diagram and an ERD?

The class diagram contains just the classes in your object model with eventual links/relationships connecting diagram elements. However those links don't necessarily correspond to physical relationships like in an ERD diagram, but instead they represent logical connections.

The class diagram is just the object model of your application and does not contain any persistence-specific information. When you think about the class diagram forget about the database or any other storage you may use.

The ERD diagram on the other side, is a persistence-specific diagram which display the entities (tables) existing in a (most often) relational database. It also displays the physical relations (and cardinalities) between those tables and all other database-specific information. The ERD diagram can sometimes look similar to the class diagram, but that doesn't mean is the same as a class diagram.

It depends on the situation where you may not like to do the ER-D. But imagine if you have a seperate data layer where the data logic is handled. In this case many details of data shall not be shared with the application layer. And you class diagram shall not go beyond the application layer. I must stress that both the diagrams are not equal. And there are situations where you need to do both, mainly in multi-tier architecture, and there are situations where you may be able to just use class diagram; e.g. single-tier application.

I strongly advocate the view that class diagram doesn't abrogate the E-R diagram.

There´s little difference in the expressiveness of both (if we just focus on the attributes, classes and associations part) if you use Extended Entity Relationship diagrams (the most common case nowadays)

True, they look very different at the graphical level since they use different symbols for the elements but the "semantics" are quite similar. They both allow inheritance (again, I´m talking about EER), n-ary associations, association classes, ...