Round 1: Royal Guard
Round 2: Royal Guard
Round 3: Royal Guard
Training is what is key here and the RT are supposedly good, but they lack well...pretty much a lot of things, namely feats and the like.
They have nice accolades, but all this amounts to is pretty much nothing compared to the Royal Guards training.
People will bring up "They were trained since birth!" and "They were obviously training to fight Jedi!"
Ok, so were Clone Troopers, yet they were still killed by Battle Droids and were noted as being less dangerous than Mandaloirians, meaning what...just because one is trained since birth doesn't give them an edge.
2nd point, ok training to fight against....what Jedi? Luke's Jedi? We have no quantifiable skill gauging of these Jedi at all, it's impressive that they are training against Jedi....but we don't even know what said Jedi they are suppose to fight can do.
There is also the point that Royal Guards also have better armor, you see the RT Stormtroopers being felled by mere blaster bolts.
Royal Guard armor can withstand hits from lightsabers and multiple blaster shots, edge goes to the Ryal Guard there. The shield the RT has is good, but it doesn't cover much and the Guard could easily bypass it.
They also have the superior weapon, the Force Pike can do all of what the Z6 Riot Baton can do, while at the same time cut through sophisticated armor like ragged cloth.
Now moving on, fighting unarmed skill....Royal Guards have that in spades, no question.
Royal Guards are noted as being able to do the impossible, they can take on small armies and escape hostile enemy planets, just to name a few feets.
Being masters of Echani(along with being masters of every martial art and weapon in the galaxy), also gives them another edge in precog, able to predict and counter the next move of the RT.
The Riot Troopers, just don't have anything really good to compare them to the best of the best of the best, the Imperial Royal Guard.