Mickey2

Are these new machines to you? I would double check threading on the 503, make sure the bobbin thread is in the tension spring and the top thread should go inbetween the two disks in the tensioner. Like Janey mentions, check that tension gradually increases from 0 to 9 by pulling the thread. It should relase when presser bar lever is up, and grip when down (when needle is up it releases too). Top tension some times needs a bit of cleaning.

Regarding bobbin tension, in my experience it often needs adjustment when going from a light weight thread to top stitch and vise versa.

For the 99, I would take out the bobbin case, screw of the needle plate and check for fluff, threads, etc. Slide the bobbin plate off and there is a lever you take to the side, it releases the bobbin case. Double check for correct threading; the only place you can go wrong on the 99 is after the tensioner, when the thread is behind the spring and inbeween the two disks there, it goes in to the hole on the small hook shaped part to the left of if, then to the take up lever. For both your models it's important that the bobbin goes in the correct way from which it is wound. The 99 can act up in all kinds of ways if it's not oiled well. Needle in flat side to the right, threads from left to right.

Feed dogs on a 99 is usually fine, but double check they are aligned with the holes in the needle plate and doesn't hit the plate when turning. Ideally they should be paralell with each other. If the teeth looks reasonably good I would suspect the problem lies elsewhere. When you take off the needle plate check that they are in firm, and not loose. Do you have the version with a round stitch length knob, or lever with reverse stitching? The 99 is a very nice machine when cleaned, oiled and set up right.