Golden Age Appearances: too many.
Both these characters were "heroic hobos," who wandered from town to town fighting crime and living a happy-go-lucky life. If you know anything at all about the life of hobos during the 1930s and 1940s you know that it was a hard, cold, desperate life, filled with misery and pain, and that it, and the men and women trapped in it, were anything but happy-go-lucky. Both the Vagabond and the Fighting Hobo are stereotypes which whitewash the sad and tragic reality of hobos during the Depression. I've included them here out of a sense of completeness, and because Michael Norwitz convinced me to, but they are shameful creations that should never have appeared.
Ronald Byrd disagrees with me about the Vagabond, and since he's very well-read in the Timely books, and wrote a good piece on the Vagabond, I'm going to include his words here:
On a strictly mundane level, the Vagabond may qualify as the strangest of Timely's costumed heroes; Namor's occasional tendency to wreak havoc in NYC notwithstanding, he is certainly the most eccentric. He is not a subterranean ruler or a robot made of rubber, he did not rise from an 80+ year old grave or gain his powers from the picture of a Greek hero, but within the realm of the actually possible, he is unique.
The Vagabond first appears in USA Comics #2, in which it is implied that, in his true identity, he is either police officer Murphy or FBI agent Walter Carstairs (Paradox for the day: How can a cop or fed (civilian identities held by a number of golden age heroes) who lives in an area so devoid of crime that he has the TIME for a career as a super-hero nevertheless find in that same area threats enough to WARRANT a career as a super-hero?), inasmuch as both are depicted as expressing frustration at being unable to deal suitably with the criminal element in Middleton in their own well-known identities, and the Vagabond debuts shortly thereafter. However, we are never specifically told that the Vagabond is in fact either of these men, only that he is a "prominent citizen." To confuse matters further, the Vagabond, in his costumed identity, is also given the name Chauncey Throttlebottom III, by which he is "better known to himself"; in effect, the captions CALLED him the Vagabond, but from his perspective, apparently, his codename was "Chauncey Throttlebottom III" (wouldn't look quite right on a team's roll call, would it?). I guess it's sort of like, when Frederick Foswell (from Amazing Spider-Man) was posing as "Patch," what was Patch's real name supposed to be? The Vagabond appears to be playing some sort of peculiar psychological game with himself (since he does not know he is in a comic book, he has no other audience), as we shall see.
In effect, the Vagabond is just another costumed super-hero with no powers other than his impressive fighting skills, except that he is wearing a literal masquerade costume (as opposed to the more customary skintight outfits that enable their wearers to be mistaken for little other than super-heroes), a tattered, padded suit (which gives him the appearance of having a pot belly) with his face made up like a clown's. He no more looks like a REAL hobo then Batman looks like a real bat---he really just looks like an actual clown, Emmett Kelly in a good mood---but as part of his modus operandi, he behaves as though he were a real hobo (When he enters a bar seeking underworld information, he asks for a job first!). For reasons best known to himself, the Vagabond affects a bombastic pseudo-upper class speech pattern (He is given to saying such things (even in private) as "Yoiks and tally-ho! A Throttlebottom sallies forth to battle evil!") which I can only assume was meant to emulate some 1940s personality whose popularity has been lost in the mists of time (oh, THEM again?).
In other words, the Vagabond (at least in USA #2-4) is not really a clownish, happy-go-lucky tramp at all; he is a perfectly respectable citizen, possibly a gainfully-employed representative of the law, who in order to anonymously fight evil DRESSES and ACTS like a clownish, happy-go-lucky tramp, which might arguably be deemed at least as offensive but if nothing else has the benefit of novelty.
By Young Allies #4, the Vagabond has, inexplicably, taken his act on the road. He appears to be indeed "on the bum," as the saying goes, with the "ah, the life of the open road" attitude that you rightly criticize, but he does not allow this to deter him from stopping a group of hijackers, and the fact that he is in fact only pretending to be a wanderer cannot be dismissed. In a truly surreal turn, Comedy Comics #11 features a character that is identified as Chauncey Throttlebottom III, the Vagabond, except that he is a cartoonish actual tramp who would pass no police or FBI examinations and could no more mingle at a gathering of the Invaders than Ziggy could mingle with Mary Worth's crowd without comment. What, if anything at all, can be made of all this is as yet unclear---the Vagabond somehow found his way into the dimension of Stuporman and Forbush-Man?---but it is apparent that the Vagabond's case is much different from that of the Fighting Hobo.