I know nothing about tennis, except if you're a professional woman tennis player, you're supposed to grunt a lot.
That said, I do know about some other sports that my kids have participated in. In some of those sports, equipment doesn't make any difference for kids at that age, in others, it makes all the difference in the world. E.g. cheap roller blades from Walmart - hit a pebble and you're going to land on the ground. More expensive roller blades: same pebble will make zero difference. Shelling out an extra $100 or so for my kids gave them a sport that they spent a LOT of time involved in (hey, it got the kids outdoors, instead of in front of the television playing video games), as well as a broken arm or two. Motocross racing - there was plenty of equipment that wouldn't have made much difference (e.g., the $8/gal racing fuel vs. the $12/gal racing fuel). And, there was plenty of equipment that made all the difference in the world, e.g., $100 every other week for a new rear tire - for the 10 year olds, this would have made a significant difference for the kids in the front half of the pack, and probably no difference for the kids in the back half of the pack.
That said, I have no clue if a $150 racket is going to make a lick of difference to a 10 year old. However, as someone mentioned with Greg LeMond, sometimes, there's a mental edge - someone might have more confidence.
One final thought: does that $150 racket have resale value IF the kid quits? A $50 racket from Walmart isn't going to sell for more than $5 at a garage sale, but that $150 racket, used, might get a reasonable return on it on ebay. It's conceivable that if you got a demo model, after reselling it if your kid quits, you could be better off than you would be with a Walmart racket.