I have two questions over here,
1. You want to be a chef?
2. You want to get into the food industry?
because both of the things are two different categories with a little overlap. While chef's work is limited to kitchen, food industry within itself consists of work like procurement, management, waiting, cold storage management, bar management etc.
If you want to get specifically into cooking and related jobs it's always preferable to get into BA Culinary Art, on the other hand if you want to see how hotels are managed from back-end to the front end, the preferable choice would be to go for Hotel Management.
While BA Culinary Arts has a narrow field of view, Hotel Management has a wide perspective. Both the courses require equal hard work to succeed.
Hope i've cleared your doubt.