Depending on the complexity of the problem I prefer to use the backend based on the following pattern:

• Frontend makes a request to run a backend function with optional parameters which the end-user specified (ie a search request).
• Depending on the parameters supplied, different functions might be run before the backend queries the third party API.
• 3rd party API response is returned to the backend.
• Backend either passes the response along or does more stuff before passing the request along.
• Then the frontend does stuff with the data based on the response received (ie there were less than 5 results so adding pagination is not necessary).

That way you can:

• Keep any necessary credentials on the server.
• Obtain logs.
• Validate on both the server side and the client side for an added layer of security.
• Use the server to filter sensitive results if necessary before they reach the frontend.
• Vary which parts of the heavy lifting are done on the server vs the device in order to improve the application performance.
• Modify your server function as needed without modifying the front-end distributable. This matters when creating a mobile or desktop app where you have to get appstore approval before a release can go live.

Well, I think I would do this on the backend. For one reason - maintainability. I'm not quite sure what your business is about, but if it's a web app right now and you plan to have mobile apps as well in the future, do it in the backend.

On recent projects I did, main reason for moving it to backend was security. If you put it into client side that usually means you also need to give api keys of the 3rd party service to the client and that means acess to 3rd party service publicaly. If api key permissions cannot be configured to match your needs then it's not an option at all

It is all about what your need is at the moment. If you access a public API, and you do not need to keep any records about user interaction with that API, you can just dump it on the client side and save up on server load. For example, if you want to put some Twitter feed in your UI, I see no reason to route this on your server, unless you want to filter that feed in some way.

If the API you call requires tinkering with the response or a special kind of request, then it belongs on the server.

What kind of calls are we talking about?