I wouldn't assume building the html on the server uses any more server resources than building JSON. Either way you are just building a giant blob of text. With html fragment caching the server could easily be doing less work this way.
Unless you are doing string interpolation to generate JSON, it is absolutely more resources... and how much will depend on the framework(s) in use. To/From JSON is a straight serialization/deserialization, where templates are a bit more involved.
It's not a crazy amount of overhead... and even then, it's a matter of how interactive the site/application is or needs to be. You can have a horrible or great UX in either direction in different use cases.
