I believe the Heller Mayflower is a re-boxing of the Airfix kit. I've never seen the inside of the box, but I have the impression that it's a generally sound, if somewhat simplified kit. (The last few sailing ships that Airfix did before leaving that segment of the market tended to fall into that category.)
The commentator in Ships In Scale is right: we know scarcely anything about the real Mayflower. I haven't done any serious reading about her in many years, but so far as I know scholarship has turned up precisely two reliable facts about her. She was of 100 tons burthen (according to a formula that was used in those days; it had nothing to do with the actual displacement of the ship), and she had topsails. (An entry in the journal kept by one of the passengers mentions that a sailor fell overboard in a storm and saved himself by grabbing the end of a topsail halyard, which happened to be dragging in the water.) That's it.
Back in the 1950s a replica vessel, the Mayflower II, was built and sailed across the Atlantic. She was designed by a fine scholar from the Massachusetts Institute of Technology, William Baker. He based his plans primarily on the Matthew Baker Manuscript (no relation) at Cambridge University. The Baker Ms. is the earliest surviving English treatise on shipbuilding; the drawings in it are just about the oldest genuine plans of English ships in existence. The ms. dates from about 1590. Baker (William Baker, that is) operated on the assumption that the actual Mayflower was twenty or thirty years old when she made her Atlantic crossing in 1620. The Mayflower II is pretty widely respected by historians for what she is: a fine scholar's best guess about what the original looked like. Baker did make one deliberate concession to practicality. Since the replica ship was destined to be a tourist attraction (as she still is), he gave her about a foot of extra headroom on each deck.
Since the fifties some people have questioned whether the Mayflower II really looks like the real thing, and I've seen a couple of other reconstructions (in the form of models and drawings). To my knowledge, nobody has ever proven that Professor Baker was wrong in any important respect. But I'm sure he'd be the first to acknowledge that there's more than one legitimate way to reconstruct the Mayflower.
On the basis of the pictures on the box, I think the Airfix/Heller kit is based on the design of the Mayflower II. (I know for a fact that the two Mayflower kits Revell issued back in the sixties and seventies were. They're superb kits.) If I'm correct on that point, the kit you've got is about as close to reality as anybody can get.
I obviously can't say for sure without measuring the kit, but that scale of 1/150 does sound too small. I long ago quit paying much attention to the claims of plastic sailing ship manufacturers regarding the scales of their products. Sometimes they're reliable; sometimes they aren't. The vast majority of the sailing ship kits on the market today are reissues of kits that are thirty to fifty years old. I sometimes think the people working for those companies today have no concept whatever of what's inside the boxes. One possibility that occurs to me is that some less-than-knowledgeable person in the marketing department may be looking up the length of a real ship in a book and dividing that figure by the overall length of the finished model - not realizing that the former figure doesn't include the bowsprit, and the latter figure does. That could lead to a pretty spectacular error.
William Baker published a book, The Mayflower and Other Colonial Vessels, which includes a nice set of plans for the Mayflower II. The best way to determine the scale of the Airfix/Heller kit would be to compare it with those plans - bearing in mind, again, that Baker's dimensions are just a well-educated guess.
That's about all I can offer on this one.