I don’t know about the more recent comics, but I read and collected the original ones. Roy Thomas and company did try to capture the spirit of Howard’s creation, and i think they did, within the limitations of the comic. They differed a bit in that comic books are a different medium, so the Conan of the comics was talkier, and they were more concerned with consistency than Howard was. Although, this being the 1970s when the comics first appeared, they were more 'politically correct". I wouldn’t call Howard racist, but his attitude was different from that of the post-Civil rights era, and he wouldn’t have had a major black character quite like Juma the Numidian.
Also, the comics weren’t quite as “spicy” as the thirties pulps were. This is highlighted by the fact that Marvel launched an “adult” magazine at the same time, called Savage Tales at the same time. The cover read “rated M”, and they had sorta nudity in it – Barry Smith adapted “The Frost Giant’s Daughter”, with the said daughter showing only slightly obscured nipplage and buttage. When they later ran the story in the regular Conan series, they covered a lot of this up.
The Conan stories, as mentioned, appeared in the pulps in the early 1930s. They were collected and republished by Gnome in the 1950s, at which time L. Sprague de Camp and others tried to connect them in a logical order, complete some, and write new ones. In the 1960s de Camp, Lin Carter, and Bjorn Nyberg contributed to a series published by Lancer books in 12 volumes that presented Conan’s career in chronological order. (Actually, Lancer folded before they could publish Conan of Aquilonia, which wasn’t published until Ace books took over the series in 1977). It was an uneven mix. De Camp had already written several histotrical novels and was a noted fantasy author in his own right, and his style meshed well with Howard’s, I think. Lin Carter’s style is very different and a little too fantastic, to my mind. Nyberg is a weird one – i don’t think he was otherwise known as a writer (I’ve only seen one other work by him) and I don’t even think he wrote in English. His story, though, is OK. (Despite what’s said above, the Lancer/ace series contains several novels by non-Howard people – Myberg;s Conan the Avenger, de Camp and Carter’s Conan the Buccaneer and Conan of the Isles. Conan of Aquilonia is a series of four stories by de Camp.)
Of course, Conan was big business, and they started putting out still more novels in the 1970s, 80s, 90s, and 00s. Karl Edward Wagner, Poul Anderson, and others wrote whole bunches of them. De Camp, who acted, I believe, as advisor to the Schwarzeneggar movie, wrote a novelization of it. These don’t always fit into the chronology of the 1960s series.
One of the more interesting was written only a few years ago by Harry Turtledove. Conan of Venarium covers Conan’s youth and early manhood, and is better than most.
Just as Bond got rebooted recently, both in the movies with Daniel Craig and in the book “Devil May Care”, because the series was getting topheavy , anachronistic, and bound by its own mythology, so has Conan sort of been “rebooted”. In the past couple of years they’ve re-issued the original stories, as originally written, out of “Chronological” order and with de Camp et al’s additions stripped away. They’ve also published Howard’s notes (that de Camp and company used to write or rewrite stories), so that we could at long last see them.