Yes, I did take a look at the pictures you sent, and it’s kind of hard to really “read” anything into them. They both look about equally sharp to me. On the other hand, the 70D has almost double the megapixels, so that makes it a lot harder for a direct comparison. Were the pictures taken using AF?
As far as broken mounts are concerned, unless your T3 is still covered under warranty, I wouldn’t bother sending it in for repairs. It’s a 4 year old entry level camera, and it would probably cost more than it’s worth to have it repaired. If you’re interested in upgrading, save your money and put it towards the new camera.
If you mount a different lens on your T3, does it have the same problems with looseness? If it is indeed a camera mount issue, then I would imagine that it would affect the way all of your lenses fit on the camera.
BTW, if you’re looking at buying another DSLR, Canon is having a Memorial Day sale…