One heck of a choice!
Having only done one, the JMT, I would say it depends on the type of experience you would like to have. On the JMT, you will start and end with quite a few people. yeah, permits are controlled, but you will other folks out there. This never bothers me much, but to some, they'd rather have a solitary wildnerness experience. By comparison, except for a few popular hikes, there aren't many destinations in the greater Northwest that I ever encounter more than a handful of people. The Winds definitely qualify. There are a lot of great trip reports on the Winds and it looks spectacular as well.
One of the best trip reports really hints at the majesty and grandeur of the Winds.
You better hop on that permit process if you hope to hike the JMT. It's definitely easier as a solo hiker to get a permit, but you could always put in a permit for the JMT and if you don't get drawn, well, the Winds it is! This year is an extremely low snow year in the Sierra thus far, so snow travel will not be an issue. I would also add that planning re-supply, the JMT experience would be easier. However, if you did a loop hike in the Winds, you wouldn't have to arrange post-hike transport back to your car.
For another perspective, this video really captures the appeal of the JMT.