The short answer is no. I found the Bose headphones slightly more comfortable to wear, and they effectively block out more noise than the Sony headphones. On top of that, I'm more partial to their sound, but those Bose models cost $300 and $350, while the Sony MDR-NC200Ds come in at $200. The price difference is significant, and enough to make the Sony NC200Ds a decent value by comparison. Not a bargain, but decent.
What'd I like about them? They're relatively compact, lightweight and good-looking. In that sense, they're more like the QuietComfort 3s, which are also an on-ear model, meaning the padded ear cup sits on top of your ear and doesn't envelope like an over-the-ear model such as the QuietComfort 15. The build quality here also seems tough enough for daily commuters, and the headphones fold up to fit into a nicely designed protective storage case (it's included along with a two-pronged adapter for airplane use).
What's also nice is that unlike the Bose models, you can actually listen to music or movies without the noise-cancellation engaged, which means that if the single AAA battery that powers the active noise cancellation dies, the music doesn't die with it.
Alas, there's no integrated microphone for making calls, but the NC200Ds feature an AI (Artificial Intelligence) noise-canceling function that switches between A, B, and C noise-canceling modes based on the intelligent analysis of ambient noise in your listening environment. It's a little tricky to test, but the AI button rendered the noisy fan in my office nearly silent, although not completely.
I also tried the headphones out in the New York City subway. Here, they muffle train noise, but the Bose Quiet Comfort 15 headphones do a better job, which we expect at their extended price point.