This is a very challenging topic.
There actually MANY physically observable differences between these two species, yet even the most experienced field tech can have trouble nailing an accurate identity to a caught mouse.
Most references will describe differences in back hair colour, tail colour, tail tufts or some other vague and subjective criteria.
So which is the best way?
According to Assistant Curator of Mammal at the Royal Ontario Museum, the single most reliable feature is the throat hairs.
If you flip the mouse over, you’ll notice both species have white throat hairs. However, if you blow on its throat, the hairs of the deer mouse are grey at the base. They only have white on about half of their length. For the white-footed mouse, the hair is fully white (see photos).
The second best feature, which is only reliable about half of the time, is the tail colour. The deer mouse usually has a “distinctly bi-coloured tail”, whereas the white-footed mouse has a “gradually bi-coloured tail”. Age and regional variety effect this feature, making it only marginally valuable.
I hope this guide was useful.