I don't have the tactical turkey edition but I've had my Mossberg 500 for a little less than 10 years now and I can say from experience that they are excellent guns. I got a new Benelli Vinci a couple of months ago and my Mossberg isn't as smooth or as flashy as my Benelli, but I've put around 10,000 rounds through my Mossberg and it's never given me any trouble. It was the very first gun I ever bought and it is worth every penny I paid for it.
I don't know much about Stoeger firearms and I'm not trying to influence you one way or the other. If you can, I would shoot the Stoeger for a little while and see how it feels to you. Like crappiepro, I feel that if you don't like the stoeger for any reason and you do decide to switch to the 500, you won't be disappointed. I have some buddies that get crazy good patterns from their 500's.