Size
The Beagle is larger on average: about 18 kg (40 lb) as an adult, against 14 kg (30 lb) for the English Cocker Spaniel.
Grooming
The English Cocker Spaniel needs more grooming, brushing a few times a week, where the Beagle needs a brush once a week.
Exercise
Plan for plenty of exercise with the English Cocker Spaniel, and a moderate amount with the Beagle.
Temperament
They differ most on independence (Beagle: decides for itself; English Cocker Spaniel: keen to work with you) and on affection (Beagle: affectionate on its own terms; English Cocker Spaniel: a lap or leaning dog).