I've often noticed that seasons 1-8 (and 9 to a lesser extent) tended to utilize a wider range of camera angles and smaller details to emphasize a gag or atmosphere, which (alongside the greater, almost exaggerated sense of depth in S1-8's animation) provided OFF in its prime with a unique visual aesthetic, as if the crude, stylized designs of the characters were being shot through the lens of a live-action filmmaker's work (as opposed to the majority of the sitcoms the show disparaged, which merely opted for broad, obligatory eye-level shots) - in essence, the show used to take advantage of its animated visuals to amplify the scope and presentation of its comedy in a way that live-action TV sitcoms of the era generally shied away from, which is definitely more than I can claim for the show beyond season 8 or so.
In a way, although it could simply have been a variety of factors (comprised episode production time and Fox clamping down on ‘off-model’ animation, reportedly), this may be related to the departure of both Silverman (who was arguably among the few '90s animation giants who managed to successfully present the technically clumpy aesthetics of '90s animation in an appealing and comedic way, particularly through the use of specific rates and types of motion/visuals to ensure a joke 'read' more effectively - think how Sideshow Bob slamming his face into a rake, technically a simple gag, is enhanced by both the exaggerated shape of Bob's mouth as he groans from the impact and the rate at which his mouth moves/the 'mouth shapes' fluctuate whilst the rest of his body remains inert, which highlights Bob's attempted 'dignity' and renders the show's work in applying a sledgehammer to his ego more satisfying/funny to the audience) and Brad Bird (who, as S1-8's 'executive consultant', basically ensured that the show's 'language' of cinematography remained unique and ambitious to further ensure a consistently pleasing visual aesthetic/that gags were presented in the correct light to illustrate their point more fully)'s departure circa the beginning of season 9 - just compare "The Cartridge Family" (the penultimate episode of both Silverman (until season 13, at least) and Bird) to even the better late-S9 episodes such as "Girly Edition" or "King of the Hill" (in which neither Silverman nor Bird were involved) produced a mere 14-15 episodes later and already the show's presentation of gags has weakened - the camera angles more closely mirror unimaginative sitcom (well, the majority of sitcom) material, the motions (legitimate animation) has become choppier and less meticulous (actions frequently occur overly quickly in a blunt manner without any buildup or integrated subtlety/aspects of characterization, which basically degenerates Homer's increasingly slapstick-prone Scully-era persona into merely a vehicle for cheap cartoon gags), the perspective has flattened significantly and the character designs appear subtly more 'obvious' and constructed (as opposed to the looser and more idiosyncratic designs of previous seasons), all of which basically accentuated as the show devolved into a shell of itself.
On a side note, you could pose the argument that the early Jean seasons (13-15) possessed improved animation quality over the Scully years (due to Silverman's return as an animation producer), the lack of comic timing in these seasons basically negates this alongside the uninspired content of the written episodes in question, an issue which also plagues the more technically fluid scenes of the most recent seasons) to the extent where the former showmanship of the show's prime has now all but evaporated in favor of flat cinematography and an awkward visual 'look'.