Loving my PS4, even if it is partially more the hardware than the games so far.
Share button is godly. I have taken so many pictures, and shared my gameplay a lot more, even more than I have since I got the capture card for console games and since I found the big picture mode screenshot button (xbox one really needs to impliment Home + RT for screenshot or something). I have a capture card for video capture so I haven't tried saving many videos, but I have to say broadcasting from the PS4 is great, much, much less painful than setting up my stream on PC. I hate streaming, but it's quite nice on PS4.
System speed is pretty great. Almost no load times aside from 1 big one at startup of each game. Game installs are a breeze, half the time the game is ready to start by the time I've inserted the disk, grabbed my controller and sat on the couch. Updates are handled great too, it checks once you launch the game, lets you play without the update, downloads fully in the background. Auto background updates in standby.
Trophies are 95% better. One, sorta big, caveat is your most recently played game doesn't hop to the top of the list in the trophy app like it does for PS3. So if you pop in an old game you want to trophy hunt in, you have to hunt it down. Also, it could use filters for which console or even search features. My trophy list is huge. Anyway, it's much, MUCH faster than the PS3 at syncing, the rarity display for each trophy is super cool (I love data porn), NO TROPHY LAG (ugh), trophies are easily accessible in game (the tacked-on nature of ingame XMB is extremely apparent on PS3).
Controller is...mmmf so good. Love it on PC too. Perfect size, had one that creaked, sony repaired it. D pad is great, might have preferred a Vita clicky style one, but this is more than suitable. DS1-3 always hurt my hand after too long; I preferred it to Xbox dpads, but it took precision over comfort. Good weight, speaker is neat and is used well (wiimote was rarely used well outside of no more heros). I don't might the light...DS4 windows lets me strobe the light in rainbow colors while it's charging, too. That's so awesome. Love the color change in games like Towerfall, the beat in Sound Shapes. Love the touchpad, been really impressed how well games have been putting the DS4 to use. Usually something little so it's not annoying, just enough to be fun and engaging.
Vita remote play is amazing, though it has a slow startup (fine once it starts, but takes a minute or two even if the PS4 is already on). Using Wifi is great for me, because my router's range is much longer than the Wii U gamepad.
Cross buy and cross save are fantastic, and one of few things that really feel better on console than PC, as far as Vita cross buy is concerned. Cross save is a bit iffy--it's absolutely perfect in theory, but a lot of devs impliment it wrong. It should be automatic (and is in Fez, Doki Doki Universe and Hohokum) but often isn't (Sound Shapes, Pixeljunk Shooter Ultimate).
Could backups are FINALLY default and automatic. My first PS3 wouldn't have ended in tragedy if it had automatic cloud backup of all content, or even if Backup Utility didn't have limited functionality restoring to a different console. I do miss Backup Utility just for paranoia's sake, though.
Media features...I frankly do not give a damn. I understand it's a sore point for some, but literally the only media features I've used my PS4 for was watching FLCL twice and watching Netflix, and that was only because my sister was over. I do feel they should fix it up so it's got everything as good or better than PS3 so they can fully discontinue the poor dear.
Basically the system is amazing. Games are coming, and since using the system, I'm increasingly annoyed at having to play games on the PS3 (or the 360 I jsut got for shmups). I think people are too harsh to judge over the game situation and media features. As a box itself I love it. Media features are probably coming, games are definitely coming. I bought it as an "investment" and am quite satisfied.