A staple of DnD has been getting access to more fantasic and powerful pets.
The 4th E Beastmaster ranger had a paragon path that allowed him a Griffon, Paladins have had access to Unicorns and Silver Dragons as mounts in the past.
A 15th level Ranger's Giant Badger is as powerful as a Griffon for all purposes except flight, so it seems like there are ways to make this even. The Find Steed ritual alludes to more powerful steeds but doesn't give any good balance rules. How do people think these should be handled?
Personally I wouldn't try to balance it with rules, I'd just add monsters/difficulty to each encounter as if an extra PC has joined the group.
Well, 5e seems to be the 'wing it' edition, so...Wing it. 
But, yeah, I'd do what OrwellianHaggis suggested. an appropriately leveled bad ass animal companion/mount is as powerful as another appropriately leveled PC in the party. Unless you want to do 4e-style stuff where the animal can only act/attack if its master spends their action to command it. (I never liked that rule, personally...It was fine for summons, but not for an independant animal...)
This is covered in the Monster Manual entries for each of these creatures. For example, from the Pegasus entry:
Noble Mounts. Pegasi are highly prized as swift and reliable steeds, being faster and less temperamental than griffons, hippogriffs, and wyverns. However, these wild and shy creatures are as intelligent as humanoids, and so can't be traditionally broken and tamed. A pegasus must be persuaded to serve a good-aligned creature as a mount, but when it does so, it forges a lifelong
bond with its new companion.
So, it requires a special adventure / quest to find and persuade a pegasus to become your mount, and you must be good aligned. Other mounts outline similar requirements. Other than that, its up to the DM to determine the specifics. Each mount type has some basic info though, so they haven't left it entirely up to the DM.
I had a character that felt the need to have a mount companion, but they were a sorcerer. So I made the Summon Steed spell a Ritual and let him take the Ritual Caster Feat. Problem solved, with the caviat that he can only have a mount or a familiar.
I would say treat them like a mix of a seconda character and a treasure/magic item/in game reward for the general case. See also: wing it.
It might be interesting to see other (sub)classes that have a garuenteed treasure/magic item/in game reward as part of their abilities, but have it count partially against their class balance, partially against their treasure balance, and maybe partially against the party balance (ie, extra opponants to battle). I could see a fighter or paladin subclass that grants them a special magic weapon, for instance.
So for the ranger, you might adjust the balance of the companion a little to follow that, maybe make it so it has its own actions.