It comes with a number of weaknesses, many of which are extremely common, it's very slow, and you have to wait until level 42 until it can evolve. You also can't get the Protector until Iron Island but by then Rhyhorn shouldn't be evolved yet. Its level up movepool also kind of sucks, mostly Normal type moves for almost all of its life as a Rhyhorn.
Here's where it begins to shine. It has ridiculously high attack and good defense and HP to boot, compared to Rampardos who has no defensive utility outside of its Rock typing. Solid Rock is also a nice ability that helps with Rhyperior's typing. Rock/Ground is amazing offensively and it's one of the best candidates for TM26 (Earthquake) since you get it so early. Rhyhorn's bad level up movepool is salvaged by the fact that it gets Rock Blast almost immediately after capturing it, and Rhyperior gets access to a lot of really strong moves, such as Megahorn and Hammer Arm. Sadly, Rhyperior gets them pretty late.
Torterra, Rampardos, Gliscor, and Hippowdon may seem like better options, but Torterra is a starter, Rampardos has to deal with its nonexistent bulk, Gliscor has an atrocious level up movepool early, and Sand Stream is an unhelpful ability ingame. Each of these have their own pros and cons over the other options available. It's hard to be awful ingame, so use Rhyperior if it seems like an interesting or fun option.
It mostly faces competition from Golem, who you catch way earlier and carries the same typing with a much better movepool from level up. Its stats are inferior to Rhyperior, but you might not even have access to it until around the end of the game. Golem isn't even considered the best option in the game either due to the prominence of the aforementioned other Rock and Ground types. Both are also really slow.
TL:DR: It's up to personal preference, but otherwise use Golem.
EDIT: I forgot Golem was in the regional dex aaaaaaaa