Whether it makes more sense to take on yoshon or cholov Yisroel is an interesting question. Putting aside practical considerations (which you can’t actually do in real life), it would seem that yoshon would come first. After all, it’s a shailah of a d’Oraisa, whereas cholov Yisroel is a shailah of a d’rabbobon. Also, the sevaros to be mattir cholov stam seem stronger than the heterim for chodosh.
However, there are a couple of reasons that some do the opposite. Obviously, there are cultural reasons.
There is also some kind of chassidishe mesorah not to be makpid on yoshon (which I don’t understand) as well as extreme importance placed on cholov Yisroel from a kabbalah perspective.
There’s also an interesting halachic perspective, which I heard from an adam gadol. Because yoshon was so hard to obtain in Europe, it was an almost universal practice to not be makpid on yoshon, and the wide usage of the heter in practice makes it more halachah l’maaseh. The heter for cholov stam, however, has a shorter history and less universal acceptance.