I currently have 2 basset hounds, Roscoe and Elwood, and a Bloodhound Pearl. Love them all for their individual traits..
Elwood we got as a pup, naturally in the woods he was great with rabbits and especially squirrels, he went nuts over them and would follow one up a tree and just stand there staring until the Marlin .22 dropped it down to him. He is now 9 and blind and his days of heavy activity are over.
Roscoe was adopted at 2 yrs old as he randomly showed up one day. Neighbor came down to get him and said she was free to a good home, he was taken from her boyfriend's cousin who abused him. He is missing 4 front teeth, one broken off at gumline, both front legs were broke, his right actually points backwards when he stands still. Arthritis in hips now at 6 yrs old because those were once fractured, had an eye kicked out of socket on top of it all. Needless to say if we ever find the guy who did this we will break his legs and teeth.
Anyways, Roscoe is still a natural squirrel hound, he will tree them and have a good old time howling at them. He cant hunt long with his hips, he takes children Asprin daily and it still gets to where I carry him to his pen at night.
The bloodhound is great at tracking, she will find me anywhere on our 104 acres if i run from her and hide in thick brush full camo. She is all nose no eyes, to the point if i run a circle and then lay down, she will walk over me following trail until it brings her back. Afraid to say we wont own another, this is our 2nd and they are a handful medical wise, we had $4600 emergency surgery when her stomach flipped wrestling with dogs after eating.
Okay so I went waaay off topic here, sorry! Bottom line, I prefer bassets over beagels because in my experience they dont bark as much, and have a deep howl versus the machine-gun bark at a high pitch. I believe with actual training, would make great rabbit dogs. As our 2 were natural insticts, they did excellent with squirrels. Besides, you also get an organic garbage disposal, entertainment, and a dog that can find any bit of food you lose when you have a basset hound.
Find yourself a Bagel and have best of both worlds. Tad bit quicker, more of a howl, will have big old clodhopper feet, an awesome nose, and a stomach that can handle a 300wsm shell.