Well, hunter vs beast master, by the book, has their damage being nearly equal if you choose certain companions (giant poisonous snake really). But that equality is 3 hp/level away from going away, and it doesn't work with Hunter's Mark. Both yours and my variants fix that.
Where we differ is that I think the animals, which were likely finalized before the DMG guidelines for CRs was completed, aren't balanced against each other. There are clear winners, and those clock in at CR 1/2 or even CR 1 in the case of the giant poisonous snake (+6 to hit, 16 AC, up to 17.5 damage, with 10 ft reach! Add on the beast master's +2 proficiency bonus and it goes way overboard). Granted, it only has 3 hp/level, and takes the time of a long rest to bring back.
You and I both agree that they need more hp. We simply disagree on the balance of the animals. I've buffed doe and nerfed a few.