This article covers the differences between both commands very well.
docker-compose up deploys everythign to the same node. docker stack deploy... will let swarm decide where to place each container.
If you're starting a local dev instance then you're technically[1] using the right command. But if you're talking about a production (or production-like) deployment, then your boss is doing the right way.
[1] I'm a big believer in using the same commands / docker-swarm modes in dev than in prod, but that's a different conversation.