Upgrading an AEM involves a lot of planning and effort. So, I would recommend moving to 6.5 directly and that way you can save time and money.
Amount of work/effort required to upgrade from 6.3 to 6.4 and then to 6.5 will be almost double the effort/work required for directly moving to 6.5
AEM 6.5 still has all the classic UI consoles available. Users will still be able to use Classic UI in 6.5.
[1] Upgrading to AEM 6.5