You've had them both for a while and they didn't take up much space. They are family. I'd keep them both.
The Kenmore can't be torn open to oil, there is no top or bottom covers. Perhaps an inspection plate on the back side, I'm not sure. At any rate just squirt Tri-Flow oil in every hole and let it soak. The same with the needle bar area and the underside. She'll free up. I have a Kenmore just like that one only in brown, a 117-812. It is one of the best straight stitch machines I have.
Oh, two things; the Kenmore turns opposite of the norm - away from you or clockwise, and the friction drive gear will be flat spotted from sitting against the hand wheel for so long. You'll need a new one before you use it.
Joe