I found another interview with the costume designer William Ware Theiss, from the July 1990 issue of TV Zone magazine, which I think supports Philipp's answer, it's just three pages so I'll post it all here:
Note in particular the second page, where he says this about the colors in the original series:
"We chose three colours - the apple red, avocado green and a sort of a Copenhagen blue - in the original series, because NBC had just gone colour, and they wanted lots of color, to sell color sets. It didn't make a lot of sense to me until we decided to break them up vocationally. I think we decided that we wanted to see more of the avocado, therefore it made sense to make that the 'command' colour, since that would be the captain and probably more people on the bridge. We made blue 'science' ... I'm not sure why, maybe because I liked the blue and the avocado together better than I liked the red with the avocado. Then the red was used for the rest of the crew, which we called - or I called 'internal services'.
Then he goes on to talk about the Next Generation colors, with the article giving a mix of direct quotes along with other comments that are presumably paraphrases of things he said to the interviewer:
"For The Next Generation I decided it was probably a good idea to keep the continuity of three colours and keep them equally distributed. But I didn't want to use those same three colours because they were not particularly becoming to a large number of people."
It's apparently all to do with the human eye's receptivity to coour combinations. "The avocado green is not particularly a good colour. Statistically, it's good on fewer people. The blue was the most becoming on the most people. The red was pretty intense.
"But by the time I did The Next Generation, I had been involved in some studies of colour and analyses of colour for individual people. So I tried to find colours that were as universally becoming as possible."
The upshot of this is that blue suits most people, with wine red a very close second, hence its use as the new 'command' colour. The mustard colour, Theiss admits, is not quite as flattering, "but it's not that bad. We used it as a balance to the other two. Two out of three wasn't bad."
In a comment, ThePopMachine objected to Philipp's answer by saying "There's no world where we cannot say that what you call teal and blue, and wine and red are not obviously much more similar within the pairs than the other way around." But I didn't understand Philipp to be saying all three colors were equally distinct from the original three, he did acknowledge that "while you could argue that Wine and Teal look similar to Blue and Red, there is no way you could argue that Lime Green is the same or even similar to mustard". And indeed, Theiss in the quotes above did refer to "wine red" and "teal blue", the big difference was the third color was originally a shade of green and now it was "mustard", a shade of yellow. The fact that he considered the former two colors more generally flattering probably was sufficient to narrow down the choice of command color to one of those two rather than the mustard, and one might speculate they chose to keep the blue shade assigned to science and medicine in order to have some continuity with the original three colors.
The Next Gen uniforms probably weren't drawing on the movie uniforms
Buzz's answer gives a good background on the design of the movie uniforms, but to expand on a comment I made there, I think it's unlikely the choice of red as the command color was influenced by the movies. Gene Roddenberry was notably unhappy with how he was largely shut out of the decision-making on the movies after The Motion Picture, and with the exception of ST IV he was fairly critical of all of them for not fitting his vision of the Star Trek universe (see for example his comment on the second page of the interview here that after TMP, 'it went downhill until STAR TREK IV'). In particular, he criticized the movies for portraying Starfleet as overly militaristic, whereas he felt it should be a "paramilitary" organization that fulfilled some military functions when needed but mainly concentrated on other tasks like exploration. David Alexander's biography Star Trek Creator, which can be borrowed from archive.org here, on p. 501-503 there's a 1981 letter he sent to Wrath of Khan co-writer and executive producer Harve Bennett, where he said that he wasn't overly bothered by smaller changes in continuity from the original series like changes in terminology, but that:
there are the more important established things which probably will affect the film’s success, since they were part of what made Star Trek so successful. Examples of these are things like the fact that Starfleet was always very clearly a paramilitary organization, and you may remember that both our title narration and our story plots placed great emphasis on exploration and seeking new life and new civilizations as the starship’s primary functions.
If Star Trek slides into becoming just a routine “space battle show” (an SF form which the critics now consider “tiresome”), then I have no doubt but that Star Trek will slide downhill rapidly. In this case, I am doubly concerned because I have an interest in this property remaining valuable.
Likewise Wrath of Khan director Nicholas Meyer is quoted on p. 410 of The Fifty-Year Mission: The First 25 Years saying:
Roddenberry definitely averred or opined that Star Trek was not a naval operation, not a military operation, it was a sort of a Coast Guard, is how he put it.
P. 543-544 of Star Trek Creator has a 1986 letter to Paramount TV president John Pike where his criticism of militarism in the uniforms extended to the uniforms:
As gratified as I’ve been with the Star Trek movies, I’ve also been very concerned with the increasing militarism reflected there. They’ve gotten by with it because of the difference in what works in movie and TV formats—and also because they’re talented people. But still the costumes, for example, have some of the movie scenes looking like a STUDENT PRINCE operetta. Star Trek was never a military show originally and a new television version will probably not succeed if we try to make it that now.
When Paramount gave him the chance to head The Next Generation, he saw that as a challenge to prove that his own vision of Star Trek could still be successful (see for example his comments on p. 546-547), and part of that vision was moving away from the militaristic elements of the movies. One of the earliest production documents he wrote was this "Creative Concept Notes" memo he sent to writer David Gerrold dated Oct. 29 1986, which includes this section:
Armaments and Militarism -- De-emphasized over previous Star Trek series and very much de-emphasized over the Star Trek movies. We go back to the flavor of the previous series first year when emphasis was on "strange new worlds" rather than space villains and space battles. True, our new Enterprise still has awesome powers in its phaser and photon torpedo banks with everything organized for prompt obedience to chain of command decisions, but the flavor of this new Star Trek emphasizes not military efficiency but rather the maturity of humanity in our 25th century in which quality of life is considered enormously more important than technological advances. Thus, we won't need Prussian guard uniforms and saluting and all that except where it is retained as a form of courtesy and occasionally as a spot of color in their lives.
And Theiss did of course consult with Roddenberry while designing the uniforms, he mentions doing so in the interview he gave the Los Angeles Times for example. So based on the above I think it's unlikely that Roddenberry desired any continuity with the movie uniforms, including in the color.