I am wondering how fast client side Javascript is compared to server side Java in terms of raw computational power.
For instance, sorting. Should it all be done server side if possible? And how about iterating through a collection?
The answer is very complex and depends on each specific situation.
A server is generally going to be orders of magnitude more powerful than a client machine; and managed code is generally much faster than scripting.
However - the client machine also usually has a lot of spare computational power that isn't being used, while the server could be running requests for thousands of users. So in that case much of the work that can be offloaded to the client is preferable.
You must understand the needs and expectations of your users for each individual piece of functionality in your application and look at the relative load versus development cost for your organization to split development between two environments and figure out what works best. For example, your users probably expect that your site does not freeze their browser or cause unfortunate "this web page is eating your computer" dialogs, so your client scripts should be written intelligently. That's not to say you can't do a ton of work on the client (you can), you just have to be smart about how you do it and remember it blocks the UI thread.