Everyone must remember that Starfleet is a military like organization. There is a command and rank structure. There is proper wear and appearance standards when in Uniform and out of Uniform. Think of the Turbolift scene Saavik in The Wrath of Khan. She was reminding Admiral Kirk that her hair was still within regulation.
Comparing my time in the Army I can briefly layout a few plausible ideas as I went though 5 camouflage patterns of duty combat uniforms, 3 PT uniforms, and 2 dress uniforms barely missing my 3rd.
If using the US military as a basis (since the show was written in the US and Gene Roddenberry himself served in the Army Air Corps), commanders have a bit of regional leeway when it comes to uniform wear. Big Army (Starfleet) decides how our uniforms are worn, but usually not when and leaves varying degrees of leeway with each uniform. During times of transitions both uniforms are usually acceptable until a mandatory wear out date. Sometimes you also have a mandatory purchase date for a minimum amount of the new uniform at the same time. US Soldiers get a yearly stipend for uniforms and buy their own uniforms. Often times uniform stipends don't cover the actual cost for uniforms. For everyday uniforms my experience has been that a transition takes about 3to 4 years from intro to completion at the wear out date for the old uniform. I know it seems overnight but it isn't as it cost the soldiers money to replace all this gear. And while we they have replicators I'm sure the idea of replacing perfectly good uniforms would be seen as wasteful.
Capt Picard was the commander of the flagship of the Federation. As the flagship his crew image is paramount when having dealings outside the federation. He could have decided to prevent the crew from jumping to the new uniform for various reasons. With his prudent command style he could have decided to wait until all the details of the new uniform were ironed out. This was a bigger transition than the collarless uniform transition. Or he simply could have decided he didn't like the look and delayed letting anyone wear it until further into the transition when he was forced by regulation. This happened with me during the first year of the woodland and desert camouflage BDU to digital camouflage ACU conversion. While in the 82nd Airborne Div (The Army's flagship division,) no one was allowed to transition to the new uniform until a new Division Pamphlet 600-2 could be written by division staff and approved by the Division Commander. 600-2 includes more guidance on the local level than what AR 670-1 provides on the Army wide level. This also allowed us to buy uniforms in accordance with mandatory purchase dates and transition to the new digital pattern mostly together and left only a few weeks of mix matched uniforms. Because of this it was a year into the wear of the new uniform before I got to wear it even though I already owned it. It could also be more granular than that. During the last year of the same transition, I was reassigned to Ft Bliss, TX. I had a Company First Sargent that set the duty uniform as he saw fit and had a field day! One week I wore 4 uniforms! Ft Bliss is a desert installation and I wore Digital ACUs Mon and Tues, Woodland BDU on Wednesday, Desert BDU (DCUs) on Thursday for Sargent Time Training, and Class A dress uniform for pay day activities on Friday! FYI during transition to the current uniform from the digital uniform big army stipulated that commands couldn't set uniform demands like this and that both uniforms would be worn side by side without local command prohibitions. Perhaps team leaders set uniform standards by the time of Generations or they were deep in a month long transition. This is what I seem to think. They delayed and were trying to make a quick transition for image.
There are other ways uniforms are phased in. Multi-Cam got phased in on a regional level prior to wear other places. As time went on it was deemed that digital camouflage was a failure. The Army needed an immediate replacement but didn't want to spend the money to immediately phase out and replace equipment that they just purchased with the launch of digital camouflage. So multi-cam was allowed to be worn only in SW Asia combat zones. (Afghanistan, Iraq, etc). Originally it was not allowed for wear in the United States at all unless in transit to those areas or immediate lead up training. Eventually it would be so popular that a variant of multi-cam would be the army wide replacement for digital camouflage in use today. It could simply be that DS9 was in a geographical area assigned to first receive these uniforms for various reasons. It could also explain Cmdr Sisko wore a traditional TNG uniform when he went back to Earth, or why visiting starships sometimes wore the TNG uniform. With Voyager assigned to that area of space it could also explain why they had the DS9 uniform as well. With time all of Starfleet could have begun the transition to that uniform by the time of Generations.
But the reality is we're all trying to force a narrative, they wanted a new look for a new DS9 series. They wanted both DS9 and TNG to have a unique identity. I think the reason to use that uniform with Voyager was because the 80's look of the TNG uniform had ran its course. The black jumpsuit had much more of a 90's feel. It was most likely cost saving to keep the DS9 uniform for Voyager. When the uniform was changed for season 5 of DS9, it was another way to not only introduce a new uniform for the big screen in First Contact, but it was again another way to differentiate between DS9 and Voyager and create unique identities besides the fact it was popular with fans.
