What do you mean the only MMOs on PS4? Have you tried the free ones? Neverwinter , Star Trek Online . I guess there's also The Division which is considered an MMO.
Anyhow, as for the 2 listed. I've played both, but they are different enough that you really have to decide whether you want something that is a typical fantasy RPG vs a 4x space sim .
I personally have a thing for RPGs like WoW / Everquest and that sort of thing, and EOS did scratch that itch on the console. EOS has been around the block for a few years now, there is a TON of content, and even more content to solo . There's all the other MMO "modes" you'd find in like GuildWars , i.e. PvP / Arenas / Dungeons/Raids and the open world PvP areas as well. The combat is a hit or miss for some (and might be the dealbreaker, i found it to be fine), but i felt the game world and theme was really well done. The quests are pretty detailed, lots of voice overs and stories to follow and areas do change based on how you complete quests etc.
Elite , well, i played it for a bit , probably better for a hardcore player to comment on this. I never really got into it, so i am completely biased on this. It took me awhile just to get going flying the ship and then doing some trade runs between star systems. I have to add, i played EVE and while i never got into the whole corporation thing, as a casual player i got really bored with the trading/mining as primary activity in EVE. Elite reminded me of this a little , but that's my personal preference. So i can't comment on the social aspect of Elite, when i played players were pretty much represented as dots on my radar or ships entering/exit space stations , i didn't see them otherwise. However i am not sure whether getting involved in group activities will change this (EVE pretty much hinge entirely on the social aspect).
EOS, on the other hand, i'd say it is probably TOO casual/solo friendly (you can level up the entire game by yourself if you feel like it, you only need a group for the PvP / dungeon activities). That said, you will see players all over the place, going about their business. On the console you will most likely hear them in the area too unless you mute the regional channels.
I haven't even started with the Morrowind expansion that came out a few months ago (the base game with the DLCs already have an insane amount of content) . So yea, i think EOS is a little underrated , people really hated on it when it launched , they expected a sequel to Skyrim, and it wasn't it. However, i think it still shaped up to be very decent representation of the Elder Scrolls world and theme.
Elite vs EOS is different enough that it really depends on what you are looking for right now. Elite seems more of a space trading, exploration and building game . EOS is a standard , almost predictable fantasy RPG.