A beagle is a tracking dog ... A german shepard is a watch dog. If you're not using them for a specific purpose, then you should research (at least) the medical problems of each breed before deciding which you want.
i have a german shepherd, and he listens great, he is very smart and playful, beagles are playful, but i would go with a german shepherd, they easily catch on, which im sure beagles can to, maybe it could be a rescuee because there are thousands of beagels and german shepherd puppies or older dogs in dog kennels, in desperate need for a home, maybe there is a local shelter near you?!
german shepherd, no kidding. These dogs, catch on better, are smarter, training isnt an issue. these dogs may have bone cancer, but other than that their fine! Beagles are hunting dogs, they can't stay off a leash without hard training, and, their nose always gets in the way, BUT they are hunting dogs so what ever lol. HOPE THIS HELPS!