Couldn’t it also be seen as similar to her S1 relationship with Matthew? Ultimately in both cases there was a worry she would only be interested in their money/prospects, and they both wanted her to marry them for themselves?
I think there is a parallel but the way the two men approach it is very different.
Matthew, I suppose, was very torn. Without having inherited Downton he would never have met Mary and realistically he couldn't appeal to her as she was in S01 as nothing but a lawyer. He could never understand her pragmatic and entirely reasonable motivations for marrying (or not marrying) or her upbringing that meant that mercenary concerns were rational. (And to be honest, they are and both Aunt Rosamund and Mary are completely right to take them into consideration. Love is all very well but a marriage survives because of other things. Mary might have been happy being married to Matthew but she would have been miserable as a country lawyer's wife, I'm convinced of it. She was right to consider the kind of lifestyle she wanted as well as her emotions. But that's a rant for another day and I'm afraid I'm as heartless as Mary in these matters!!) But to Matthew, the idea that she would consider marrying him for any other reason than disinterested love was completely unpalatable. As Mary would mourn later, he saw the world in a very black and white way. His own disinterested love for her was beautiful but it did not allow for the shades of grey in Mary's character and there will always be a sliver of doubt - Mary says that she would be with him "on any terms" but at the end of the day she never had to make that decision... Her behaviour in S03 prioritised Downton over Matthew on several occasions and S04 shows her continued devotion to the estate and her and George's inheritance. Nothing bad about that, but one has to wonder...
Charles' position and attitude is very different. He recognises with a pragmatism equal to Mary's that she can have her pick of men and situations and that she is in a very strong position. He is up against a man with a title and social status, Gillingham. And he could compete - he could say, "You give me an estate turned into a girls school; I raise you a vast inheritance in Ireland" etc etc and he could tempt Mary materially. However, he has the confidence not to do that. He recognises that these things hold weight, that they are important and important factors for Mary as a widow with a child and property to take into consideration and he chooses just to present himself - sometimes abrasive, often clashing ideologically - and see what she makes of it. He confronts the issue head on and makes it a personal challenge whereas Matthew was rather afraid of it. At least he was uncomfortable enough with it to accuse Mary's reluctance to agree to marry him on that rather than actually listening to what she was saying or considering that actually status means a lot to her and maybe that's okay.
Actually, Mary is in a stronger position in S04 anyway. She already has Downton sorted. She doesn't need a husband with an elevated position now or a large fortune or an estate. Those are things she can bring to the table. Actually, I think Charles' inheritance in Ireland poses a massive problem to them rather than something particularly attractive!