When Illustrator traces an image it searches for details and creates paths, and it does it pretty well, it never has the sharp detail of the original photo but I like the artistic look it applies.
Vector files store all their information as mathematical values, allowing them to scale to any size, this means a small vector image's file size probably won't differ very much from a much larger version of the same vector image. This also means they can't be compressed.
Pixel based images can be shrunk and optimised with various techniques that essentially trick the human eye to see it satisfactorily, whilst progressively degrading its quality the more you modify the same file (not from master file).
Now, simply knowing that, you can logically deduce that if an image has a lot of detail, there will be a lot of paths, a lot of mathematical data and a large file size, conversely, if the image has few details, it won't require that many paths and won't be so big.
So to conclude, it depends on the image your tracing, and the file it's coming from. You may end up with a similar file size, but I doubt you'll end up with a smaller file size unless they're very basic shapes like a simple square.
Additionally, it's kind of redundant to compare the file size of different formats that serve very different purposes and have very different qualities.