I tried both of them and it was pretty the same results for processing messages.
I used webhooks/rest/webhook if I want the complete run of RASA (NLU + Core). I use it in my main application.
For an other tool, I only need intent classification (for some testing purposes in the “how to improve our models”), so I only use HTTP API so no actions is triggered.
API also exposed other informations like version, models, etc. This could be problematic in terms of safety if you exposed your API to the outside.
Thanks for sharing. I think it’s an inspiring idea that using the HTTP api when training the model and for the chatbot side, using webhook will be an easier choice.