In theory, yes all level 3 courses are on a par. However entry requirements are more than about levels; it may also depend on the knowledge acquired ie content of the course. So it depends on what DC want to do afterwards...
In the case of the pre-degree Foundation Diploma in Art & Design? Access to this is usually via an A level in an Art & Design subject. It is a one year course, that involves experimentation within art & design to find one's strengths & interests before applying to a degree course.
Increasingly however, students are applying straight to degree courses & skipping the Foundation course. Provided they know which area of design they want to do, and their portfolio is good enough, they can do this...
Your DD's real choice is between choosing a range of subjects via the A level route, or a BTEC Extended Diploma in Art & Design, Graphic Design, Fashion Design, or whatever. Choosing the BTEC route will involve specialising straight away. Is she ready to do this?
Because the BTEC route is FT Art/Design, there is less need to explore within design & therefore for the Foundation Diploma. It would be more common to go straight onto a degree course from them.
So before deciding, I would want to know:
Is DD 100% sure about a career in Art & Design? Has she ever considered other careers? What does she know about careers in this area ie how much research has she done & is her knowledge realistic?
If she is academic, and there is any doubt about choice of career/degree course then choosing the A level route would be safer. It would allow her to keep more options open, providing she didn't choose: Art, Graphics & Textiles! She would only need one A level in an Art/Design subject to apply for an appropriate degree course (or for the pre-degree Foundation course, if she decided she wanted to do that)...