I have and always will believe that Cristiano edges Messi, and this is 100% not because I don't rate Messi, if not for Cristiano, he would be the GOAT and I probably enjoy watching Leo more than Ronaldo.
Scoring Record
Ronaldo is one of the most consistent scorers in the sport’s history, with over 650 goals for both club and country, including 120 Champions League goals, a record number and a once in a lifetime achievement in itself. Forwards such as him are often lumped into two archetypes: Target men who play with their back towards the goal and rely heavily on their team mates to assist them, or penalty-area poachers who finish off opportunities by feasting on half chances, rebounds and scraps.
Abetted by a natural ability which is enviable to most other players (as is Leo) Ronaldo is able to combine those two categories into a lethal goal-scoring package. Ronaldo is more economical than most others, to use a cliche, a "Clinical Finisher." He has a tenancy to slot home the big chances, no matter how big the stage. Ronaldo has also worked hard at developing a unique technique when striking the ball, whether with the inside or outside of his foot , so that each time it leaves his foot with more of a wobble than a swerve. This makes life very difficult for Keepers.
This combined with his excellent positioning is responsible for his high goal scoring tally. Michael Owen said "It doesn't matter how good a finisher you are if you're not capable of working your way into positions to get chances."
Confidence and "Mental Strength"
Maybe this is a left of field point to be making, but as someone who works in the field of Psychiatrics, I believe that Cristiano has adopted the perfect mindset of an Athlete, one which allows him to produce the Audacious moments we have all enjoyed from him .He dares to attempt what others won’t even consider, and that he routinely makes the impossible, possible. He plays with such little anxiety, even in the face of abject failure. While his team mates often let their shoulders sag in the face of seemingly insurmountable obstacles, Ronaldo views this as an opportunity for greatness.
Evidence to my point, Ronaldo's two goals in their 3-0 Win over Juventus in the quarter final, particularly his audacious bicycle kick that had everybody talking. It is rare to see someone convert a bicycle kick, 99 times out of 100 it doesn't come off. Buffon didn't even attempt to save it, he was glued to the spot, so perfectly placed was Ronaldo's effort that a GOAT goalie contender was helpless to stop it. It was so unreal that the home fans honoured him with a standing ovation, a real sign of greatness (see the other Ronaldo at OT.)
In the words of Barzagli "It was a Playstation goal, When you play against him you need perfection. As soon as you leave him something he punishes you."
Good in the Air
Ronaldo has so many ways he can beat the keeper, whether its a shot which makes the ball swerve and bobble tempestuously, slipped in at the near post, a free kick, a penalty, but one which makes him stand out is his Aeriel Ability. He is incredibly muscular yet slender, allowing him to routinely out jump defenders in order to win aerial challenges and score spectacular headers. If I remember correctly, there was a University that determined that he can jump 44 cm from being stood still and 80cm when he gets a run up, which was more than your average NBA player. His heading ability gave portugal the Upper hand in their semifinal against Wales in 2016, when he lost James Chester and scored a powerful header to give Portugal the lead.
I remember the commentators stating that he lept around 2 and a half feet in order to head the ball, which meant that he was about 8,7 feet in the air when he met it.
Adapting his Game
Ronaldo has evolved and subtly changed his game over time to suit both his age and the changing face of football. While he was with us and his younger days at Sporting, he was used as a pacy winger normally down the right side. He would use his incredible natural pace and flamboyant skills to take defenders on one on one, and race to the by line to deliver a cross. He was already a top player, but there were little inaccuracies and inconsistencies in his play that allowed "he's nae good at this level" pundits like Souness to belittle him.
His first adaption phase started towards the end of his time with us, when Fergie played him down the middle in a more attacking role, as a forward in our 4 3 3 or behind the main striker. This change of position allowed him to develop into the prolific goal scorer he is today, and his finishing became much more efficient. He became a relentless attacker who would play all over the front line, coming at the defence from all angles. This new Ronaldo continued to develop at the start of his Madrid career, being played from the left but given free license to roam as he pleases.
Over the last 3 - 4 years we have seen another adaption in his play. He has bulked up, particularly in his upper body, increasing his strength and stamina. The physical aspects of his game have improved, allowing him to retain possession for longer periods. He still scores with alarming regularity, but the efficiency of his runs and movement has improved greatly. He has become adept with monitoring his stamina, and making those decisive runs when needed so he can create and finish scoring chances. He drops deep to receive the ball much less.
Ronaldo the Leader
This is something that again, he has developed with age. He is still capable of petulant moments, see this champions league final, but more times than not, he comes up big in the important matches. In his last 4 finals he has scored in each, including two goals in 2017.
He is a valuable on the pitch leader, using words and his style of play to raise the level of those around him. In the 2016 Euro final he was absolutely cleared out by Payet, having to be stretchered off after half an hour. The sight of him on the bench encouraging his team mates, pacing up and down the touchline while carrying a nasty injury has been a historic football image.
Weaknesses
Just to show I'm not too much of a fanboy, I thought i'd include this section. He is not a perfect player, and reluctantly deals with defensive duties (perhaps why Jose had no interest) he often can't be bothered to track back to help out his teammates, or dot he unglamorous work that is required of him.
He is still, unfortunately, a bit of a diver, very skilled at engineering contact and is a regular winner of free kicks and penalties, going down despite his impressive physical stature. It works a lot, but I think refs have cottoned on in the last 2 to 3 years meaning that he doesn't get away with it quite as much as he used too.
Conclusion
Ronaldo is one of few players in history who can turn the tide of the game all by themselves. He is capable of scoring in any game and in any situation.