It's difficult to truly say just how often this has happened.
First, in many cases, the characters created by a creator (especially when you go back to the 1960s and 1970s) were almost always considered to belong to the company, not the creator. So, if the creator explicitly stated that the character in question was supposed to be Character X they had created at Marvel or at DC, then there would be immediate legal issues involved.
Marvel over ownership of Blade.
If the creator has never explicitly stated it, then it may be very hard to say with certainty that character X at Marvel is "really" the same character as character Y at DC (or Image, or whatever). It's not uncommon for a creator to create titles similar to what they're best known for when they move from one company to another. Around 1980 or so, Marv Wolfman moved from Marvel to DC. While what's he's best known for from that period is The New Teen Titans, he also created Night Force. Prior to the move, one of the things he was best known for was Tomb of Dracula at Marvel. Night Force was similarly steeped in the supernatural, and there are characters in the two that are at least vaguely similar. Does that mean that (for example) Count Winters was really Quincy Harker moved to DC from Marvel? I'd say certainly not; however, I'd be surprised if there isn't someone out there who'd argue the point.
Note: I'm ignoring topics such as:
- authorized crossovers of characters published by two different companies;
- cameo appearances, where the character is usually not appearing in their most recognizable form, and the appearance is mostly intended as a joke/easter egg (For example, Clark Kent has been seen as a bystander in multiple Marvel comics over the years, easily recognizable by his 1970s/1980s standard outfit (blue suit, glasses, red tie));
- characters who are creator-owned, and whose adventures have been published by multiple companies (Dreadstar, for example);
- licensed characters who have been licensed to multiple companies over the years (The Shadow, Doc Savage, Tarzan, et al.); and
- "homage" characters - characters who are obviously intended to be versions of another company's characters, as an "homage" to those other characters (most notably Squadron Supreme and the Shi'ar Imperial Guard).
(I will note that, over the years, certain "homage" characters have wound up as the leads of series; past a certain point, I think they aren't really actionable any more. Consider the JMS Supreme Power/Squadron Supreme series Marvel was publishing as an on-going series for several years. While the characters involved were originally barely disguised copies of the Justice League, these characters had been Marvel characters for decades at that point.)
All that said, I can think only think of two cases where the creator fairly explicitly stated that character Y was really the same character as character X published by another company.
The first was the Mantis/Willow thing noted in the original question. Steve Englehart had created Mantis during his run on Avengers at Marvel, and had told a long-running story culminating in her being the "Celestial Madonna". She married a plant pretending to be her late boyfriend, and they went of to do whatever (yeah, it sounds weird - because it was).
When he moved to DC and was writing Justice League of America, he decided he wanted to tell a story that was basically about Mantis' pregnancy - that was the Willow story in JLA #142.
Actually, the story gets even odder than that. Englehart later wrote Coyote and Scorpio Rose for an independent publisher, Eclipse Comics. In Scorpio Rose, he included a character named Lorelei, who was fairly clearly supposed to be Mantis/Willow after her child was born. (To make sure you didn't miss his intent, Lorelei lived in Willimantic, CT (not certain about the state, but I am about the city name).
Just to close the loop: Mantis was basically unused at Marvel from when Englehart left, until, well, he came back and wanted to use her again. She appeared in (at least) Fantastic Four and Silver Surfer in the late 1980s (her previous appearances having ended by the early 1980s). After his use of her, she went unused until Englehart brought her back yet again in his Avengers: Celestial Quest mini-series in 2001-2. Finally, someone else brought her back: Abnett and Lanning used her in their Guardians of the Galaxy series in 2008, which lead to her being in the "Guardians, Vol 2" movie.
The other instance also traces its origins back to Marvel in the 1970s, and to a writer named Steve. Steve Gerber created a character named Howard the Duck while writing Man-Thing for Marvel. He was well-received, and was given his own comic, initially also written by Gerber. Gerber was eventually fired from the book for missing deadlines, and moved on to other assignments at other companies.
When he heard Marvel was looking to license his creation out, he sued Marvel for ownership of Howard. The lawsuit was settled out of court, with Marvel owning the character. Given how some of those licensing deals went (the "Howard the Duck" movie, specifically), Gerber may have been fortunate.
However, Gerber had a chance to write a Spider-Man/Howard the Duck team-up (Spider-Man Team-Up #5) in 1996. As it so happened, he was also writing a crossover for Image, pairing his character Destroyer Duck (who was basically created to help finance his lawsuit in the early 1980s), and Erik Larsen's Savage Dragon.
There was an semi-official crossover in that story: both stories involved a fight in a Cleveland warehouse, with the characters from the other stories appearing as silhouettes. Marvel, however, was not happy when they read the Savage Dragon/Destroyer Duck comic. Gerber had added some scenes were the Howard silhouette was cloned. According to his story, Spider-Man went home with one of the Howard clones, while the real Howard (and his girlfriend Beverly) were in the SD/DD comic at the end. Howard changed his name to Leonard, and Gerber had "stolen" Howard back from Marvel.
He never really did anything with Leonard from there, and in fact wrote a Howard the Duck mini-series for Marvel's MAX imprint a few years later.