All 2D-to-3D converters are not created equal, and the conversion technology is improving. That said, I suspect you'll get better results from your TV than from the player. This opinion is based entirely on your mentioning that your player is a Panasonic. I've seen conversion results on two Panasonic players and was not impressed. I've also read several posts from Panasonic users who say that the player does nothing more than generate a double image of the entire picture, with no attempt to distinguish objects within a scene, so that the "3D" is nothing more than the illusion that the entire picture appears to be behind the TV screen.
You didn't mention the brand of TV. I've been surprised by the number of positive comments on the 2D-to-3D conversion in the latest LG passive 3D TVs. In fact, I haven't come across a single negative review.
My own 2D-to-3D conversion is software-based (home theater PC and PowerDVD 12 Ultra) and I can vouch for the fact that this technology is improving significantly. I wanted software-based conversion so that I could take advantage of any improvements without waiting for a firmware upgrade that might never come.
The technology has improved to the point where some movies look as if they were custom-converted. Some of the more impressive real-time conversions are with Peter Jackson's KING KONG, STARSHIP TROOPERS, and the Raimi SPIDERMANs. I've watched the SPIDERMAN 2 train fight between Spidey and Doc Ock dozens of times. And the Kong / T-Rex battle scenes are downright amazing in faux 3D -- I'd say they are the high point so far.
I'm curious about some of the "black boxes" like the 3D-Bee that seem to be getting good reviews.