There are a lot of limitations with Amazon's hosted offering. Mostly you will find out about them when your cluster needs maintenance (upgrades, outages, etc.). Elastic cloud is a much better product in terms of features, support, performance, documentation, price, etc. I've used both and ran my own clusters as well. Elastic Cloud is my default option these days.

Can you say more about these limitations? Right now I'm using a pretty big custom ranking function to rank my documents in Elasticsearch (using a function_score query), but maybe I'm misunderstanding.

Sorry, I was a bit vague. Queries are fine, but you cannot, say, use a scikit-learn model trained on user activity.