Using the statistics you provided, I can try to compare them:

**Cristiano Ronaldo**:
Total goals: 714
Total appearances: 1037
Goal-scoring rate = Goals / Appearances = 714 / 1037 ≈ 0.69 goals per game

Total assists: 221
Total appearances: 1037
Assist rate = Assists / Appearances = 221 / 1037 ≈ 0.21 assists per game

**Lionel Messi**:
Total goals: 681
Total appearances: 862
Goal-scoring rate = Goals / Appearances = 681 / 862 ≈ 0.79 goals per game

Total assists: 283
Total appearances: 862
Assist rate = Assists / Appearances = 283 / 862 ≈ 0.33 assists per game

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Messi won the 2022 World Cup in Qatar with Argentina, while Ronaldo won the 2016 European Championship with Portugal. As you mentioned, Cristiano Ronaldo is the all-time leading international goal scorer, which is very notable accomplishment. Although, Messi has won more Ballon d'Or awards (7) than Ronaldo (5).

In the end, deciding who is better between Messi and Ronaldo is still a matter of personal preference, but the data shows that Messi has a slightly higher goal-scoring rate (0.79) than Ronaldo (0.69), as well as a higher assist rate (0.33 vs. 0.21), and considering the achievements won, it looks like Messi is the better player.
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