It’s the age-old debate which seemingly will never have an answer… or does it?
Until last year, the pair had dominated the Ballon D’or award for 10 years – winning five times each – before Luka Modric finally broke the chain.
And both players contest the FIFA Best player of the year award with Liverpool’s Virgil Van Dijk, who won the UEFA equivalent last month.
But there is little question over who the greatest players currently active are – even if it has proved difficult to separate them.
However a look at what some of the football greats have said down the years paints a different picture – and one clear winner.
Here’s what they said…
“Messi. I would have loved to continue playing alongside him.
“I didn’t get enough time with him, he was very young. I’d love to take to the pitch with him one more time.
“He’s the best in history, no doubt. Nobody has done what Messi’s done.
“I hope he plays 20 more years. Those who love football would love to have him here for much longer. I think when he leaves, nobody will be able to take the No 10 of Leo.
“For me it’s not a question over who is more complete, it’s a question of taste. I prefer Messi’s style.
“The other one [Ronaldo] is complete, he has it all. So does Messi, but it’s a question of taste and I prefer Messi’s style.”
“I played alongside Leo, so there’s my answer.
“I have an enormous amount of respect for Cristiano, as someone who maintains such a high level for several years.
“It’s one thing to have a good season, and then have another four years later but to keep up with that level for consecutive years is something else.
“People realise it, of course, but I feel like we still don’t grasp the real measure of what these two are doing. In the future, people will look back in awe at the continuity, the goals and the pressure that comes along with doing this for so long.
“So I’m full of respect for Ronaldo, but I played with Leo and had extraordinary moments with him, we lost and won together, so that is all I have to say on Leo.”
“Messi is much more a team player than Cristiano is. He scores but also produces many assists. For me as a player, Messi is better. There is a big difference in being just a great goalscorer and being the best player.
“Every person that understands football knows this. It’s absolutely ridiculous to me that some people actually think Messi isn’t the best.
“This isn’t about Cristiano at all. He’s a fantastic player, one of the best goalscorers ever. This is about how ridiculously good Messi is.”
“They have similarities in their technical skills and talent, and it is amazing for football to have them both present, but Messi is simply the best player in the world.
“He [Messi] is alone in his class as a player, it is impossible that there is another like him. He, like Cristiano Ronaldo, who is not at his level, are both above the rest.”
“Watching Messi against Tottenham at Wembley made me think about the Messi and [Cristiano] Ronaldo debate again.
“Messi [is the best] but Ronaldo is brilliant. Ronaldo is sensational at what he does, with pace and power.
“He scores, he takes free-kicks. But as an all-round footballer, Messi – wow, his passing – has absolutely everything.”
“Ronaldo’s an extraordinary footballer, but Messi is a genius.
“There are three geniuses in football: Pele, Maradona and Messi. Period. Ronaldo is very strong as he lets you win everything, but Messi is a genius and something else.
“I faced Messi when he was 16 years old and I was amazed. He did the same things he does today but 20 years younger because he was born a genius.
“He invents things that others don’t see. Ronaldo has made himself a champion, but not a genius.”
“I think they’re both operating on a different planet to every footballer that’s ever lived, probably besides your Peles and your Maradonas.
“But Messi for me is more of a team player.
“If he’s in on goal he’ll look for a pass as well as obviously posting really, really good numbers individually as well.
“Ronaldo for me is more individual. He’s hungry for goals, he’s a little bit more selfish, whether that be in a good way or a bad way and obviously the profile of the players is very different in terms of size.
“I think they’re different in many ways but what I will say to them, and the biggest compliment I can give them, is they’re operating on a different planet than any other footballer out there at the moment.
“I go Messi. I’m not selfish, I’m a team player.”
“Messi does more things compared to Cristiano. Messi is the best. If Cristiano considers himself the best player in history, that’s fine, but those of us who see him train, there is no comparison.
“Messi is the best in history and we don’t see it any other way. Messi is the difference-maker and we always tried to give the ball to him in space with time to unbalance them. Messi is the player that makes the most difference in the world. It’s more than obvious.”
“I would still stay with Messi. Scoring is important, no doubt, but if you do not have anyone to prepare, then the ball is not enough. For my team I prefer Messi.
“Messi’s been the most stable in the last 10 years. As for Cristiano Ronaldo, he’s a great goalscorer.
“Ronaldo’s been able to score goals, while you see Messi creating goals and directing the play, as well as scoring.
“Ronaldo’s a great goalscorer but in terms of the complete player, there’s no doubt that Messi is the best.”
“I never thought I’d see a better player than Diego [Maradona].
“Maradona was unbelievable and I was so much in awe of him, as everybody was in those days.
“But I think when you look at Messi, he does everything and more than Diego could do.
“I’m also a huge fan of Ronaldo, I’m a massive admirer of him.
“I think he’s one of the greatest goalscorers of all time, there’s no question about that.
“But for me football is about watching it and getting joy from it, and when I watch Messi play it makes me feel joyous.
“He does four or five things in a game that just get you off your seat, and for me that’s the difference between the two of them.”
“That’s the difference with Messi. Leo is a phenomenon, we never talk about Neymar… but that side of Cristiano, of training, professionalism, focus, motivation, success… Cristiano has an advantage over all the others.”
“I think Messi is one of a kind. What he’s doing, I don’t know if we will see another player do the things that he does.
“It is different [with Ronaldo] because he is the result of hard training. It is not natural.”
Sir Alex Ferguson
“Now don’t get me wrong, Messi is a fantastic player, it’s like he’s wearing slippers when he controls the ball. But here, for me, is the difference. Messi is a Barcelona player.
“But Ronaldo could play for Stockport County and score a hat-trick. He just wanted to be the best in the world.”
“I was a big fan of Maradona growing up and of the current crop Ronaldo is good but Messi is the best I’ve ever seen. I don’t dish out praise lightly but Messi deserves it. I look for weaknesses in his game and I can’t find them.”
Best of the rest
Paulo Maldini : “Messi or Cristiano Ronaldo? I would say Messi even if Ronaldo is phenomenal, but the Argentine is the essence of football.”
Robert Pires : “I have played with Zidane, Henry and [Juan Román] Riquelme, and against Ronaldinho and Cristiano, but Messi has something that nobody else has. I don’t know if he is the best in history, but there are few where he is.”
Arsene Wenger : “Who is the Best Player in the World? Leo Messi. Who is the Best Player Ever? Leo Messi.”
Gheorghe Hagi: “Messi or Cristiano? Cristiano Ronaldo is very good, but I prefer Messi. He’s incredible.”
Michael Owen : “I can’t believe anyone can have played the game of football as well as Messi.”
Luis Enrique : “Messi is the best in the world without any doubt and for me the history of football.”