The crossed rifles patch was awarded when a soldier displayed great proficiency with firearms. Should the soldier advance to higher rank via certain requirements and exams, a crown would be added above the rifles to denote their expertise. Currently, the Royal Military College of Canada awards their top marksman of the year this crown of honour.

I'm less confident about the crossed axes. My first instinct is that they're the badge of the sapper, a type of military engineer typically dispatched to build bridges, maintaining air and roadways, erecting friendly domiciles and other day-to-day facilitation. Here is a brief history of the Canadian sapper; my apologies it isn't more academic in nature, but it's a pretty good summary of the Canadian sapper and a few sappers of note. It also includes a few academic sources if you'd like to check it out.

Another possibility for the crossed axes is the Assault Pioneer Platoon. These soldiers were similar to the sappers, but also were responsible for demolitions, booby traps, and other incendiary devices in the field.

http://imgur.com/8a9piuk here is a link to pictures of the patches