I just made the jump this year to the PS4 version of the game. Been on the PS3 version thru MLB 15 The Show. Still have my PS3 though for my teenage son. So, I have the 16 version on PS3 as well for him.
I've compared versions & playing on both consoles. No doubt a much better experience on the PS4. However, after playing several games & downloading several different rosters for 16 on PS4 I still think MLB 14 The Show is the best game of the series & that's on PS3 for me because I didn't get a PS4 until I got MLB 16 The Show.
MLB 14 The Show plays smoother than any of the other versions of this game. SCEA still hasn't fixed all the problems with the PS4 version after 4 patches. Don't think there will be another patch either. It's still a very fun game but there's still way too many bugs with this years game on PS4.
The 16 version on PS3 plays a lot better than the PS4 counterpart. Of course, the graphics aren't even close but overall the game is better on PS3. However, not all of the same features are available on PS3 either.
I've played my son one on one a few games on PS3 & he's beaten me a couple of times & I've beaten him a few times. He's not as long a veteran playing this game as me.
I've played it ever since it first came into existence. He's only been playing since about version 13 of The Show. He's soon to be 15 years of age. He's actually pretty good on the PS3 version.
He tried to play me on the PS4 version but found it pretty quick he was way over his head.

I'm still not good enough for my liking on the PS4 version. I have a franchise going with my Braves but haven't played but just a few games.
My record is 3-9 which is about right for the sorry Braves. I've played 9 of those 12 games with the other 3 simulated. I've scored double digits 1 game so far.
I beat the Marlins 11-6. I've given up double digits in 2 games myself. Once to the Nats & once to the Marlins. Bryce Harper in that double digit game hit 2 HR & drove in 6 runs.
In my one offensive double digit game Gordon Beckham hit a 2-R HR, 2B,& single with 5 RBI's. Teheran got the win but gave up 5 ER's in 6 innings of work. I was up 9-6 when he left the game.
My hitting isn't that bad with the Braves. It's my pitching that sucks. I have the worst ERA in MLB thru 11 games at 6.86. I'm hitting .275 as a team which is middle of the pack in MLB.
Beckham leads the team with 4 HR & Freeman has 3 HR. Beckham also leads the team in RBI with 12. Freeman is 2nd with 10. Freeman is only batting .244 though. Beckham is batting .298.
Teheran is 2-0 but his ERA is 5.72 in 3 starts. Bud Norris is 0-3 with an ERA of 7.33 in 3 starts. Vizcaino has 2 saves in 2 opportunities. His ERA is 4.24 because in his 3 appearances total he can't get them out without getting into trouble and/or giving up a run or two.
I'm sure I will be calling up Swanson & Albies later on in the year as my franchise goes. Probably make some trades as well.