Auto summarisation only creates classful summaries, which is really unflexible. With manual summarisation, the network administrator has ultimate control about precisely what the summary address should be and what interfaces it should be advertised out of. This is the best and most flexible option. Auto summarisation by large is considered obsolete and its use is discouraged in any environment.
From IOS 15, the auto-summary is disabled in cisco devices. Personally, I don't recommend to use.
The advantge of the manual summarization is that you can apply by interface in your network (very specific), instead of the auto-summary where is applied in the entire device (all interfaces in the eigrp process)
More information: https://netfixpro.com/eigrp-auto-and-manual-summarization/
The options that you could implement is the manual summarization and the stub eigrp to reduce the routing table (it is the goal in the design)
The short answer:
Auto-summary is classful only, disabled by default (on modern routers), and would generally be avoided
Manual summary is whatever you want it to be, and is applied to 'choke-points'. There's no need to area boundaries like OSPF has.
So, try to identify 'choke points' in your network, and apply summary there.