If you don’t use the mapping features and you don’t feel limited by using your GPS watch, it might be worth saving a couple of bucks and sticking with your watch.
If you want something that’s more purpose-built for cycling, or if you eventually want to use mapping features, then a bike computer might be a better choice. A bike computer may also have more data fields you can add to your screen that are relevant to cycling, as @JonGreengrass said. They can be nice to have for cycling-specific workouts too, as @ArHu74 mentioned.
Ultimately, it’s your choice! I’m a big fan of the navigation features commonly found on cycling computers – like @Hristo, I’ve done a ton of cool rides I probably wouldn’t have done otherwise thanks to the ease of having route directions right in front of me.