It all depends. Every even-numbered year has a major sports event. They all call it "the biggest sports event." The World Cup, The Olympics... And then there are European Championships. And in the odd-numbered years the U21, U19 championships etc. take place.
Then there is Formula1, considered as "the biggest circus on earth," well right... All those sponsors for teams and individual pilots and even team managers, their banners, flags, the flags of the event itself, yellow caution flag, blue "let the better driver overtake"-flag ("you are being lapped, shame on you"-flag in other words), red "stop the race"-flag and the checkered flag of course... And many more. People who are in love with the noise of 800BHP F1 cars run to the tracks, with their ear-plugs, ironically.
The Americans consider the NBA champions as "The World Champions." They do the same in "their games" such as baseball, "Football," and ice hockey too. Their "Football" is not even close to the football us Europeans understand, so they call ours "Soccer" but who cares.
In Turkey for example their "Football" is being confused with "Rugby." I guess it would bother them if they knew, 'cause they are different games. Well yes, "Football" is a different game too, if you ask me.
And then, there is the Champions League. Some of the biggest sports events I mentioned above are totally international while some are continental, some even national. But ever since people started travelling no game has managed to stay national in any way.
Of course there are many traditional games performed mainly by certain nations' citizens but when it comes to popular sports mentioned above, such as football (or soccer you may call it if you insist), basketball, volleyball, tennis, F1 etc, you can see every possible color on any flag available on this blue planet.
And Champions League is so-called European organization held by the UEFA. But the top 32 clubs competing in its main group stage consists of roughly 800 players which are from all over the world, literally. UEFA makes announcements against racist actions at the beginning of every game which is played under this very tournament, indicating the number of nations being represented on player-base in the competition, pointing a finger on how extensively international the tournament is.
This year 17 nations are represented on team-basis in this top level competition of Europe. And you can be sure that nations represented on a player-basis are much more than 17.
For the past decade you can talk about top level football in three nations' leagues, The Premiership of England, La Liga of Spain and Serie A of Italy. Definitely many may argue that this list must be extended such that it will include Bundesliga of Germany, Ligue 1 of France and even BWin Liga of Portugal, but this is my personal top three.
UEFA does not disagree with me based upon their coefficient lists and therefore these above mentioned nations supply the most number of clubs to this cream of the crop competition. You can watch the top three, even top four of these domestic competitions in one game, along with the ones of others. And it also allows many underdogs which may turn out to be surprise packs such as this year's CFR Cluj or Anorthosis.
And Champions League is far far away from being "Purely European." When you watch a national game of Brazil against Argentina for example, you feel sorry for their players, who have to fly all the way back home from Europe just because most of them are playing in the old continent. (The presence of foreign players and regulations on this case is totally another point of discussion which I tend to touch soon enough.)
So for me, right now, Champions League is the greatest sports event taking place and its being held annually makes it even more interesting and appealing. You don't have to wait 4 years to watch it, and it is a huge international competition that provides you the utmost level of football and performance, in front of passionate fans from all over the continent, in all kinds of tiny to huge stadiums.
The hymn of the competition is what you want to hear when you are standing on those stands, while the logo of the competition, a huge ball made of stars is being waved by the kids, in the kick-off circle.