I've played a handful over the years!

When Subeta was relatively new on the scene, I tried to play it, make goals, note my favorite pets/colors. But I wasn't very captivated... the art a little too complicated, designs not as simplistic as I prefer, and I didn't have a sense of the greater world around these creatures like I did with Neopets... didn't have favorite lands or environments. No particularly fun gameplay aspects I liked either... Though I remember its methods of displaying/sorting pets being pleasant, and I believe individual pets could have little collections of items, which is stimulating. There wasn't a way of accruing wealth I actually enjoyed... and no pets I was so in love with. I couldn't really 'develop' OCs within Subeta.

Aywas is another I played, for a bit longer than Subeta! I actually drew some of my Aywas at the time...
But weirdly the issue with Aywas was that, the alluring factor of it for most users was entirely customizable art... as in you could pay an on-site artist to have essentially your OC as a pet, and you could also pay to BREED given pets, including original ones, to produce some amount of babies (there were also lesser breeding coins to basically just apply a simple filter between 2 standard pets)...
I don't know how to put this, but this watered down the integrity of the world to me, and I didn't understand the 'point' of this level of customization, in terms of how I engage with petsites...? Imagine if you could just have some Elden Ring dragon on Neopets... If you could put any OC on the site, what did it mean to be 'Aywas'? I liked some of the stock critters you could find, but nobody else was really interested in playing this way, and of course the site's monetization relied mostly on these custom options. I had a weird feeling that I was playing it wrong...
I remember liking ? exploring for pets ?

Flight Rising I played for a bit, and I have an account there still, though I don't touch it much anymore. I don't find the art appealing, on the whole, and the specbio summaries of species make me feel insane (making little to no sense, as a person who loves specbio ...) ... but the breeding aspect is interesting and I like how that is programmed! I enjoyed combining unlikely pairs. I have some precious and weird dragons I drew (in my own way...) years ago. I have a lot of art of Spirals and Tundras in particular!
Flight Rising is funny... the fact the place you purchase dragons from is called an 'Auction House' made me imagine a sordid sort of world. I think within the canon of Flight Rising I'm a lunatic doing depraved and isolate things in a discreet location. The lore is so self-serious I want... to... humiliate the dragons... ? It's an odd relationship, me and FR...

I don't like wolves so Wajas is nothing to me... "17 different canine breeds" worthless.

Lioden is fine to observe, lions are cute. But I can imagine lions inside of my own mind to my own satisfaction, so I don't see a purpose for me to play it.

ChickenSmoothie is... the least of them probably?!? ldfjkl;g;kf I extremely can't engage with it... have never really understood what goes on there...

Never played goatlings either, I think this genre of petsite can't allure me, even if it is something I love, like goats... I can imagine many goats more interesting than this...

CHILDHOOD STORY is I remember a girl I knew who played a petsite that was horse-centric, but it was ... based on like, buying and selling horses on a fake ebay style site ???? and it used pictures of real horses ?????????? I could not UNDERSTAND it...

Anyway after all of that, the takeaway is that I am interested in bespoke worldbuilding, an appealing, inspiring place to play in. Neopets captivated me by creating a lot of examples of, wild and crazy shit going on around all corners of the world... the 'Gallery of Evil' was very exciting to me, and it let me imagine all kinds of things that COULD exist, like Balthazar, the Jelly Chia, Spider Grundo. Beyond that, the entire world, things suchas the Deserted Fairgrounds, Turmaculus... someone like Eliv Thade exists out there.
A right balance of showing me examples, and leaving a lot open to the imagination... I like setting my OCs in different lands, even different points in Neopian history (like before the fall of faerieland, or pre-moltara discovery)...

Obviously it isn't a petsite, but Pokémon definitely achieves this same sortof thing to me! Enough evidence of some strange or odd things, like an island of all pink Pokémon... even the flavor text on cards alone made my mind wander in fun ways, ponder how different things could intersect, what might occupy the same environment...!

Livly Island has a fun balance! This history of alchemy, a slightly different world from ours with a little more magic... an ecology of the pets... but, evidence in the NPCs, of varying levels of intelligence of Livlies, a lot of poorly understood and mysterious elements. The various lore behind some islands, like the Mandrake, or Love Laboratory, fun to roll around the mind... Rambles as larval livly...

'Petsite' is a broad genre, so many have different goals, purposes! Some focus more on fostering a community between users... some are more about gameplay itself... or customizability of the pets... there are degrees of context or lackthereof for the pets. Some are very restrictive, others are very open. Whatever petsites anyone likes probably derives from what aspect they want to interact with, and how.