This is a bit of a hobby of mine. I find HoC makes more sense to me, but I mostly agree with PP that your experience will depend a lot on how experienced the consultant is. I have been done several times, originally by myself then in groups to encourage friends and as part of a corporate induction experience.
The HoC approach gets me correct every time.
I would recommend both colour and style, once you have the hang of those, how to select makeup will be obvious. I thought that colour would make the most difference for me, but it was once I got the style, too, that people started to spontaneously compliment me. I agree with a PP that getting someone really good will make hugh difference, regardless of which system they use.
Loads of people, including my mother and sister, can pick their own colour and style and were astonished that I couldn't. Now I have been shown how it works, I have really got the hang of it, I find it really easy.
Since I got it done, I haven't bought anything which is wrong, so now everything goes together. I never need different shoes to work with a new outfit, as my existing things will work. I don't have to buy whole outfits, as my existing things already work well.
Enjoy.