The Lantern Ring's by far.

Yeah, the lantern ring is more powerful by far. 
 
The Mandarin is kinda like Wonder Woman, his weapons are decently powerful, but he's dangerous mainly because he can Chi amp his body to the point of surviving Iron Man attacks, and smashing Iron Man's armor with karate-chops and kicks and whathaveyou.
 
 The rings mostly allow him to do middling stuff like create a bunch of psionic illusions. He then charges in and kicks Iron Man in the nuts while Iron Man is fighting things that aren't there. Basically, the rings are pepper-spray, blinding the other guy. It's Mandarin's Chi powers that make him truly dangerous.

madrian does have rings that allows him to disintegrate matter as well as mentally control people. that out does the lanterns ring power

Can't read the OP, but I disagree with some opinions here about Mandarin's rings not being powerful and only used to compliment his martial arts or chi. He might use them that way, but that doesn't mean his rings aren't powerful. The impact beam ring smashed Rhodes as Iron Man through a mountain and the impact was felt thousands of miles away. His ice blast ring can freeze the molecules of an object or person with absolute zero temperatures. His disintegrator ring literally weakens the bonds that hold molecules and atoms together. His heat blast is considered a doorway to the center of stars and his electric ring taps into static energies on a planetary level. The black light ring taps into the same Darkforce dimensional energies that are used by Darkstar (who has restrained high tiers) and Cloak. He's also got a ring which can molecularly rearrange molecules of matter for transmutation. He's turned men into cockroaches, statues into soldiers, mountains into servants, etc. The spin/spectral ring decelerates time around you and grants you Quicksilver level speed. It bends the air around the user to make them appear ghastly. There's a reason why Malekith himself lusted after these rings. They pale in comparison to Green Lantern rings, but they're still extremely powerful.

That is Fraction's bullshit. That ring has always caused tornados, not speed. The Mandarin's super-speed comes from his martial-arts and mastery of chi-amping his body. Hence him being able to use super-speed without wearing the rings, and Temugin also being able to use super-speed without wearing the rings.

Fraction tried to diminish Mandarin by retconning his innate abilities into ring-abilities. But since his story only has one picture backing it, and Mandarin having that speed innately has multiple issues under multiple writers backing it, and back that that ring creates tornados, the bulk of continuity does not yet support his retcon.

@tem_borjigin: True, I never really looked at it like that, but Alec Eiffel did have the spin ring and not only did Tony confirm that it gives them "Quicksilver level speed", but he was also shown to punch Malekith half a dozen times at once which also led to him losing a tooth. But yeah Fraction made Mandarin look like he was useless without the rings. Hell, he even writes him as getting killed by Stane. A multiple mountain leveling explosion couldn't even do that.