Hi,
The main difference is that the Appointment Hour Booking is “services oriented”, it allows adding services with a defined duration and the available times are calculated based in the “open hours” and “service duration”. The “capacity” is defined for the service.
The WP Time Slots is “time-slots oriented”. It allows more freedom for creating separated time-slots each one with its own capacity (capacity is defined for each time-slot). There are no “open hours” in this one but multiple time-slots added at the needed times.
Based in the above both plugins covers different cases of use.
The other features and plugin interface are very similar.
Thank you for your interest in the plugins!