Ronaldo has won the competition five times, once with Manchester United and four times with Real Madrid, while Messi has won it four times with Barcelona, where he has spent his entire career.
The Juventus star told DAZN (h/t Football Italia):
"The difference with Messi is that I played for several clubs and won the Champions League with different clubs.
"I was top scorer in the Champions League six seasons in a row. There aren't many players who won five Champions League trophies, so this is why I feel that I can identify myself with this tournament.
"Messi is an excellent player who will be remembered not just for his Ballon d'Or wins, but also for having improved—like me—year after year.
"I wake up every morning with the idea in my head of training with the objective of achieving something more, not just to earn money. Thank God, I don't lack money, so what I want to earn is a place in the history of football."
When Barca won the Champions League in 2015—Messi's fourth title, albeit a hamstring injury kept him out of the 2005-06 competition from the quarter-final stage onwards—Ronaldo had only won it twice.
However, the Portugal superstar has made the competition his own in recent years with three consecutive victories at Real Madrid from 2016 to 2018.
This year's final between Liverpool and Tottenham Hotspur was conspicuous by the pair's absence:
Ronaldo is the competition's all-time top goalscorer. In 162 appearances, he has netted 126 goals, 65 of which came in the knockout phase.
Messi, two years younger than the 34-year-old, has played 135 times in the Champions League. In that time, he has returned 112 goals, with 46 coming in knockout games.
According to Opta, of players with at least 20 goals in Europe's premier competition, the Argentinian has the best minutes-per-goal ratio having found the net every 99 minutes on average.
They are streets ahead of their rivals when it comes to braces and hat-tricks, too:
In the last campaign, Messi's semi-final first-leg free-kick against Liverpool was voted the goal of the tournament, while Ronaldo scored a contender against his former club in the group stage:
Given Ronaldo's accomplishments in the Champions League in recent years, Messi's similarly excellent contributions have perhaps been a little overlooked.
Having not lifted the trophy since 2015, the Barcelona star will be desperate to add another medal to his collection this season.
Juventus will be pushing just as hard to win it with Ronaldo, though, and if they can avoid the kind of upset they suffered at the hands of Ajax in the quarter-final last season, they have an excellent chance of doing so.