The 401 is a good bit more complex under the hood than the 403. The 2 knobs controlling the cam stack selectors are the main difference where the 403 has none of that and only requires to change the single removable cam to select the stitch type.
The 401 does have some features not available on the 403 though: the straight stitch needle position (AK3) allows the needle to be positioned incrementally any amount left or right of center where the 403 has Left, Center, and Right positions only.
The 401 has 7 built in "primary" cams that will behave exactly like the corresponding 403 removable cams. In addition it has the 'S' or Special position that allows you to insert any of the special cams the 403 will use. In 'BS' position, the 401 will behave just like a 403 with any of the removable cams.
Where the 401 gets confusing though is the 'combination' cam positions. All these settings are described briefly under the cover on the 401 but may help to understand a bit more by reading the few pages in the manual to understand. The 'Combination' settings combine 2 different cams and here the stitch width control behaves differently than for the "Primary" cams. The middle position '3' combines the 2 cams effect equally. Towards 1 favors one cam, towards 5 favors the other cam..... All this for some decorative stitches that few are ever likely to use.
The other common problem reported on the 401 (and 500) are the selector knobs become frozen. This is due to the grease drying up after 50+ years on the selector posts. (because no one really uses all those decorative stitches anyway....) Clean off the dried up grease and oil the posts. The problem will be fixed for at least another 50 years.
They are both great machines. Get the one you prefer.