What e-commerce platform or framework are you using?

A lot of this depends on what your infrastructure already supports. Either of the options are a great choice so it comes down to what will be easiest to integrate and which search service is most affordable.

Elastic search is open source but you will need to configure and maintain it on your server. It may be more difficult to set up depending on the platform your app is built on.

Algolia has great documentation and is normally pretty easy to integrate but it can be pretty expensive.

I've never used Typsense but it seems like it would be a great option as well.