Aiden and Carrie were never suited. Carrie wants Manhattan, fancy restaurants and It Girl lifestyle, not hill-billy country life, not even with a rich furniture maker. He wants a trad wife. The only man Carrie ever really cared about was Big. Every other guy she was with was in some way being compared with Big, but it always came down to what Big wasn't giving her and those men were, as opposed to a pure interest in those men.
Aiden: The rebound after Big's marriage. Devoted to her, and put her on a pedestal, unlike Big. She ignored all their fundamental incompatibilities because she couldn't be alone while Big had Natasha. She looked at Aiden through the frame of how he was different to Big, not who the man actually was. And she ended up cheating on him because she was more attracted to Big and what he had to offer, even more so when it was forbidden fruit.
Aiden part 2: After Big left for LA. Carrie alone again. Aiden not interested and acting rather Big like, with his Big cigar and Big money invested in Steve's bar and his Big aloofness. She wanted him when he was being like this. Not so much when he reverted to his old ways of eating KFC in his tighty whities.
Berger: She was at her most lonely (and arguable most vulnerable) when she got together with him. But she was still speaking to Big constantly and there was phone sex, which she had to put an end to, but not until she was already romantically involved with Berger. His main purpose was as a male reflection in the mirror - a writer, a trendy guy about town, a glittering male counterpart to her, just as she went from column writer to book author. Went to shit as soon as his career went to shit, because his ego was as fragile as hers.
Petrovsky: The older man who offered her all the things that Big didn't: romance, keys to his apartment and the grand life that she'd wanted from Big. But all entirely hollow, because she was running away from her feelings for Big again the whole time, not seeing Alex for who he was - a selfish, self important, snobbish prick who, once again, was wholly incompatible with her.
Aiden Part 3: Once again on the rebound (from Big). Once again it's all about comparing him to Big, and deciding she made a mistake with Big, rather than looking at the man in front of her and how their relationship might work now as mature people with different histories. That 20 years together line in the last episode shows you her mindset. She's not seeing Aiden now, she's rewriting the past. Shoehorning herself into his marriage and kids, including not caring he slept with Cathy because she's more or less in a polygamous relationship with all of them.
Big was a complete arse, but Carrie was always pushing him for more than he wanted to give and trying to break down his barriers, like a stalker. He was older and had been previously married, and made it clear he needed to do things in his own time and they were not in the same relationship place. It would not surprise me if his going to Paris and marrying Natasha was an escape from Carrie's intensity. He did come good for Carrie in the end, and I agree that the "jilting" was more to do with Carrie once again pushing him and not listening to him (his not wanting a third, 3 ring circus of a marriage). He gave her many years of faithfulness and made her massively wealthy. I find Carrie's erasure of him now beyond distasteful.