As with all dog breeds that exist today, development and refinement was due to pairings of other breeds. It often takes centuries for a breed to stand out as its own breed, at which time no other bloodlines are introduced.
The Beagle
was developed from several other breeds which are thought to include the Talbot Hound which was derived from the St. Hubert Hound, North Country Beagle, Southern Hound, and possibly the Harrier. After many decades of development, by 1830, Reverend Phillip Honeywood established a Beagle pack in Essex, England and is credited as this being the basis for all modern Beagles going forward from that time.
With the Basset Hound, one of the ancestors is also the St. Hubert Hound, as mentioned above in regard to the Beagle, so it is here that it makes sense that these two breeds are similar in several ways. With the Basset Hound long body and short legs, it is believed that a mutation in litters of a breed called the Norman Staghound was also involved, and that breed was also a descendant of the St. Hubert's Hound.
Quite a bit of refinement took place in the 1870's in France with additional development later taking place in England.
In regard to health, both breeds are prone to certain issues.
The Beagle is considered a rather healthy breed. Common health concerns include epilepsy,
allergies, eye issues, hypothyroidism, hip dysplasia and back problems. While rare, Steroid Responsive Meningitis (SRM), also referred to as
Beagle Pain Syndrome is a serious issue that can be tricky to treat.
With the Basset Hound,
common health issues seen with the breed include osteochondrosis, Dissecans (OCD), bloat, elbow dysplasia, thrombopathy, eye issues, von Willebrand's Disease (vWD), and hip dysplasia (CHD).