If I measured as a US size 7 on the Brannock Device, which US size should I pick in an Adidas boot or a Nike boot?
Looking at the Brannock Device sizing chart here, it appears that no further information is given other than the shoe size.
Unfortunately, feet are all very different and the problem with a specific number is that it assumes certain proportions between foot width and length, as well as arch type and other differences.
Furthermore, not only is there variation between manufacturers, different manufacturers' individual products also vary widely.
I am roughly a US size 14. Adidas Copa Mundials in US size 14 fit me perfectly. However, Nike's range of US size 14 indoor football shoes I find are a little short and feel very tight on my heels and toes, even though they fit the width of my foot perfectly.
You will need to try a range of products by a variety of manufacturers to find a boot that fits you well. The best advice I can offer is to stick with the same boot once you have found one that fits you comfortably and works well for your playing style. A lot of time and money (in purchasing shoes that end up not working out) can be wasted if you switch to a new product every time your boots wear out.