I like to compare old-style numbers to lowercase, and new-style to capitals. Some typographers even talk about 'lowercase' and 'uppercase numbers'.
To my eyes, using UPPERCASE in the middle of a sentence seems odd, also when using numbers in the text. old-style numerals just 'flow' better with the rest of the lowercase letters in a sentence. When available, I see them as the 'default'.
Contrarily, uppercase numerals do serve their purpose when large amounts of numeric data are collected in e.g. a table.
The 'zig-zag' is no more than with regular lowercase letters, as Bart Gijssens comments. Take the sentence you just read: the words 'regular' and even 'zig-zag' (including the quotes) are all over the place as well.