I'm in the process of replacing TeamCity with Azure Pipelines (not my choice). It's ok but I also doubt it's best in class, TeamCity is far better IMO (more flexible, more informations/actions on one screen, less clicks, better logs display, better tests results display, live tests results, etc). I wish they had an hosted offer, and yaml configuration.

Can't find the discussion now on GitLab, but I recall comments claiming that Azure Pipelines is very flexible, and GitLab CI's new task DAG should be modeled after that.

They just added it in preview within the last couple weeks.

You can bodge your own solution if you use your own build agent.

For hosted build agents, this is about to change, as a new caching task is in preview. I've tried it, and it's unstable at the moment, so I'd recommend just waiting until it's out of preview.