Why was DS9 in the Alpha Quadrant using the old TNG style phasers but Voyager and Equinox for that matter were using the Compression Phaser Rifles and Voyager even using the new FC Rifles (for some reason). Also why did Voyager and Equinox only carry those Compression Phaser Rifles but no other Starfleet Vessel... Other than those 2 security officers that beamed aboard the Prometheus in "Message in a Bottle"
DS9 and the movies didn't use the Voyager rifles because the producers wanted to keep Voyager and DS9 as separate as possible to give them distinct identities as shows. This also translated to no Borg stories for DS9, very limited references to the Dominion and the end of the Maquis in Voyager, and a general seperation of props and sets. Despite all the ships in the Dominion War, we only ever saw one Intrepid class ship (the USS Bellpheron) in exactly one episode in the 7th season, and DS9 had to fight to use it. And we never saw an Intrepid class (or a Soverign class) in the big battle scenes. They were off limits. It was only in the CG era when they started to share ships Alpha Quadrant ships (when Voyager rarely showed them), but that was because of shared universe stuff.
DS9 did use the FC Rifles on at least one occasion as I recall, and Voyager did late in its run as well. The likely reason for their limited use was prop availability for the FC rifles (of which only some of them are "Hero rifles" that could be used in close ups). First Contact was filmed in Spring/Summer 1996. Insurrection was filmed in Spring/Summer 1998. DS9 Season 5 and DS9 Season 7 were filmed at almost exactly the same time with Season 6 being in the year in between. It's very likely the reason is as simple as the FC rifles were tied up in the TNG movie productions and the TNG rifles (or rather the DS9 modified versions of them with the reticle) were plentiful and availible. As I recall, Voyager only showed those FC rifles in its last two seasons, which were filmed in 1999 and 2000, between TNG productions.
Kind of supporting this point is that DS9 and Voyager often used the First Contact Tricorder after it was introduced, but also regularly used the second TNG Tricorder along side it. Again, likely because they only had so many "Hero props" they had to share around three simultaneous productions.
That's the most likely real world reason.
In universe, probably because Starfleet had them stockpiled and crews were using what they had available. It's worth remembering that the Cardassian Wars were little more than border skirmishes compared to what would come with the Dominion War, and that war deeply scarred the people involved. Starfleet was not a military organization in the 2350s and 2360s. But the Borg encounter in "Q Who?" started to make it one. We're supposed to believe from various sources that the compression phaser rifles, quantum torpedoes, the USS Defiant, the tactical systems of the Soveirgn class, most of the "Battle of Sector 001" ships started to transform starfleet into a potent defense force for maybe the first time ever (something that would fortuitously, save it during the Dominion War). That process wasn't complete by the early 2370s - the Federation fought the Dominion War with a lot more 100 year old ship designs than it did late 2360s design. The whole transition process didn't anticipate a major war. As Shelby said "we thought we had more time" due to how far away System J-25 was.
In universe, look at the Admiral Janeway future of 2404 (so 5 years after Picard Season 1). Federation defense technology had taken a quantum leap forward compared to the 2370s to the point that it had a torpedo that could destroy a cube in a single shot.