Overview

Most cloud providers have some form of dedicated transcoding service that is specifically designed for that purpose. AWS has Elemental MediaConvert, which lets you run "jobs" to transcode videos to different sizes, and provides an absolute ton of options.

Use cases

Transcoding long videos, or transcoding to high resolutions

For any transcoding job where a serverless code function isn't powerful enough (which is likely to be a lot of them), a dedicated transcoding service is your only realistic option. 

Transcoding at speed

As dedicated services like this are provisioned with very powerful hardware, to be able to perform any transcoding job, they will finish a given job much faster than a serverless code function will. 

Limitations

Cost

Dedicated transcoding isn't cheap, and the pricing can be quite complex. It will cost three or more times the price of an equivalent job using a serverless code function.

Increased development overhead

While setting up video transcoding via a serverless code function is hardly "simple", setting up video transcoding in a website context with a dedicated transcoding service is even less simple.

The services themselves are easy enough to use, but you need to integrate them with other services to know when a job has finished, and process the results, and they usually have their own APIs you need to make use of.