Before we dive into this subject it is VERY important to note the biggest differences.
First, ALL memory optimized indexes MUST be created when the table is created or migrated. You cannot add indexes in an existing table without dropping and recreating the table.
Secondly, currently you can only have 8 indexes per table including your primary key. Remember that every table must have a primary key to enforce a secondary copy for a minimum of schema durability This means you can only really add 7 additional indexes so be sure to understand your workloads and plan indexing accordingly.
There are a few other differences as well, which Monica covers before detailing the specific index options.