The plots are very similar; a young woman, deeply in love with a young man, disdains marriage, but is finally convinced to wed the man, and finds her prophesy of unhappiness is coming true. In both films, we have past lovers who interfere with the marriage. But there are substantial differences, and those changes mpact the remake.
Illicit makes quick reference to Anne Vincent (Stanwyck)'s reasons for disliking marriage - her parents were divorced. The only other parental figure we meet is Dick's father, who is a good and kind man. No spouse is ever mentioned for Mr. Ives, Sr. As a result, Anne's reluctance to wed is rather unspecific. Ex-Lady, however, gives us a clearer picture of Helen Bauer (Bette Davis)'s abhorrence to marriage. In one brief scene, we are shown the horrible marital example Helen has lived with her entire life - her domineering father, and her passive, obviously abused, mother. Given a graphic example of Helen's family relationship, it's little wonder she despises marriage. Also, unlike Anne, Helen is extremely career-focused and has a marketable skill. We have to assume that Anne is independently wealthy - we never actually see her doing anything.
On the other hand, the reason for the couple's separation is much clearer in Illicit. Dick and Anne are never with one another. They are always partying, and the intrusion of their exes is much more evident. Another big factor is Dick's obvious lack of a career or of any kind of ambition (other than carousing). In Ex-Lady, Don's jealousy of Helen's more successful career seems to starts the downward spiral (though Don was aware of her work ethic before their marriage).
While Ex-Lady is 12 minutes shorter, there is more depth to the characters. We never felt that we got enough screen time or development of Ricardo Cortez' Price in Illicit. Monroe Owsley, however, gets much more of a chance to flesh out the "other man, " Nick, who he portrays as a total swine; he's oily and rather revolting. When Ricardo Cortez plays the same character, you don't like him, but he's not quite as slimy, though he should be.
All in all, we love Stanwyck, we're not keen on Raymond, but Ex-Lady came out with a slightly higher thumbs up from the group. That extra bit of character development, and the strengthening of the lead female role made the film a lot more appealing. Here's a scene from Illicit.