Can you elaborate on why AA with API call takes too long to run?
After setting up Launch/Analytics/Triggers/Pipelined for abandoned cart, direct AA/AC calls would be my preference as it is relatively simple to set up.
That said, Triggers does give you quite a bit of flexibility on triggering rules as well as trigger enrichment from Launch/AA. You can also have multiple JS handlers on the AC side to process different triggers, so if you want to add new Triggers, its fairly straightforward to implement new data. Triggers can be very confusing to set up correctly, especially around encryption of PII data if you intend to send that across. It also has a bunch of data concurrency issues with the data it sends across. Also, the setup documentation for Triggers is seriously lacking up to date content so can get confusing.