When you're looking for a new game to really stretch your competitive muscles in, whether it's to just take a break from your main game or to swap games entirely - one of the most important things to do is look at the games that are currently dominating the online activity charts. It's hard to train in a game without any players, and more importantly, if there's no way to train - there won't be any competitors to play against.
Currently, the most popular game on Xbox Live is exactly what you would expect it to be - Call of Duty Black Ops II. The competitive scene for this game remains every bit as strong as it was at launch, if not stronger, and the ability in this game to actually be matched up against people of your skill level in league play has made it easier than ever to practice Black Ops II and compete.
The second most popular competitive Xbox 360 game online is FIFA 13. While it might not seem like there is a ton of competition for this game in your part of the world - particularly if you love in the United States, FIFA is played competitively in Europe on a regular basis, and has indeed become one of the biggest competitive games in a short time, thanks to its massive popularity online and therefore its huge player base, many of which have the ability to play at a competitive lever after a bit of training.
Last but not least is Halo 4. While the MLG may have eliminated the Halo part of their tournament, competitive Halo play is still alive and well in many other leagues, and indeed all around the world. There may not be as many people playing this as are playing Black Ops II, but if you really want to compete in Halo 4, there is plenty of practice and competition to be had.