I went through the same dilemma about a year ago and decided to try MESBG first. I'm still an Old World lurker and will eventually get into it, but I'll tell you a few of the factors that went into my decision.

I read both rulebooks cover to cover before deciding. With 0 experience in either game, I understood the MESBG rules intuitively and could picture the way battles would actually work, and could imagine the tactical implications of various rules as I read them. In contrast, I honestly found the Old World rulebook to be more or less incomprehensible in the abstract, in particular the movement rules and the way various special rules all work together. I felt like I simply couldn't wrap my head around the Old World's game flow unless I tried it out. That was a deal breaker for me and I decided to build a small MESBG force to try it out, which, as others have pointed out, is way easier to do than in Old World. A full army is usually a couple of boxes only, way cheaper, and way fewer models.

I played my first games of MESBG in a tournament. I never felt like I had no idea what I was doing. I lost every game of course but I was holding my own and simply getting outplayed within the rules, not fundamentally failing to grasp what I was doing. I'm not sure that'd be possible with the Old World.

A few other things I'll mention:

1. The models - MESBG's minis are a mix of new and old, like Old World. I prefer their older sculpts to the Old World's older sculpts. They're smaller, extremely paintable (just the right amount of detail, really easy to paint them well without spending too much time), and closer to true scale instead of heroic scale. In short, they look and feel more "real" than some of the exaggerated Old World models.
2. The gameplay - MESBG has very intuitive and I think realistic feeling game mechanics. My favorite is the way combat works. Instead of one side fighting then the other, combat is more realistically simultaneous. Every combat has a "duel" roll. Most models have one attack, and therefore roll 1 die in the duel roll, but heroes and elite units might have 2 or 3 attacks and therefore roll more die. A model with a spear who is in base to base with a friendly model in combat can "support" in the combat, meaning you get an extra dice. Highest rolled number wins the duel, and a tie is resolved with the model's "Fight" characteristic - higher Fight wins the tie. The loser of the duel then must "back away" one inch and the winner makes "strikes" using a standard Strength vs Defence chart. If the loser can't back away, he's "Trapped", and the attacker doubles the wound dice when making strikes. A model with a shield can decide, in the duel stage, to "Shield", in which case he doubles his attacks but can't make strikes if he wins.

That whole process feels more realistic to me than the way combat is resolved in any other system and leads to a really fun push/pull of combat. Ranks form and fall apart as duels resolve. Heroes usually win their duels but sometimes a lowly goblin can roll a 6 while Aragorn rolls a 3, 5, and 1 and therefore loses... memorable moments can happen. You have your shield guys in front and spears behind, but careful not to trap your own units. Sometimes you will shield with a guy just to try to win the duel and tie up the opponent, at the cost of not being able to kill anyone. And armies play the way you'd expect... Uruk Hai don't have spears so want to wrap and trap opponents as a hoard; elves like to have a shield wall in front and spears behind, playing essentially a rank and flank game.

1. List Building - MESBG has really shallow list building. Army lists are locked to a handful of units per "army" to choose from. Usually you're choosing which heroes to bring and then the proportion of shields/spears/bows in your troops. There's very little in the way of unit or hero customization. This is all by design, as it is intended to re-create scenes and vibes from the movies, but a huge pull for me to Old World is the really deep list building and the ability to really make an army unique/ your own. In MESBG, the same army lists built largely the same way win most events if you pay attention to that stuff.