I feel like in terms of hardware they were largely the same. I'm sure some tech expert can explain why I'm wrong, but I never noticed a major difference when I played at the eyeball level.

In terms of software, PS4 has an edge. But for multiplatform games I would usually buy them on XBox simply because I liked the controller better.

For me, the PS4 comes out slightly on top simply for Spider-man.

I remember the days when different consoles in the same gen were so unlike each other that multiplatform titles were totally separate games on say SNES vs Megadrive or N64 vs PS1, or looked radically different like PS2 vs Xbox, so I'd say PS4/XBO were very close in terms of the visual end results; usually it was 900p vs 1080p which isn't a big gap to my eyes.
Same goes for PS3 vs 360; the best stuff on both was of a pretty similar level of graphical quality.

Really comes down to which first party games you liked better.

Ps4. I think PS4 is thee best console of all time with thee best catalogue even if it is in need of a few ps3 titles like MGS4, still. It's topped the ps2 for me right around the time Ghost of Tsushima dropped, the biggest titles have been a bit samey and a lot of the unique games fell flat but they're still there for anyone who wants to play them and then you have the PSVR catalogue which, on it's own is beastly. I've never seen a console do this well, in my mind at least and I've been around since 4th gen.

IDK about all that. The exclusives on ps4 blew most xbox games away other then red dead 2 which was only 864p on xbox. Also 640p looked like crap in comparison to 720p 360/ps3. some games are also 720p on xbox  and 920p on ps4 also a huge gap there, not to mention stuff like skyrim, and bayo there was some massive gaps in how the game looked and played ps3 vs 360. just look at this night and day differnce.

The differences between PS4/XBO and between PS3/360 are quite minor compared to the old days; back in say the 4th, 5th, or 6th generations the differences tended to be much more pronounced.

i see what you mean but if you do compare ps4 best looking games to xbone best it's a pretty big gap in quality. Also the consoles weren't being released at the same time that plaued a huge part as well.

Halo 4 is an interesting case of... Style over substance.
Geometrically many things in Halo 4 were scaled back compared to Halo 3, they also dropped the tessellated water and the double buffer... And brought forward the texture and mesh streaming from Reach.

It very much used a baked lighting pipeline... But because of those cutbacks they were able to implement subsurface scattering for some impressive skin shading.. This is actually a form of Ray Tracing ironically enough.

But it wasn't anything the Playstation 3 couldn't do.

Gears was just a showcase for Unreal Engine 3.5, to me it wasn't anything special, it was a good looking game no doubt for the era.

Playstation 3 offered higher performance, it was just difficult to achieve maximum throughput.

The games performed better on the console that was easier to develop for. It's not rocket science.

It's actually the same issue the Xbox Series X faces... Due to it's split memory pool speeds, it's actually a harder console to develop for verses the Playstation 5 (Ignoring the Xbox's API issues as well).
Thus the 20% performance advantage ends up being irrelevant.

Calling it a Xbox 360 with a twist wouldn't be far from the truth.
Nintendo made some bizarre hardware choices with the WiiU... Which ironically would benefit the Switch console greatly when it came to porting WiiU titles.

The fact that multi-plat games aren't able to fully utilise that advantage isn't a huge deal, since they at least aren't much behind PS5 (if at all) compared to PS3 which was a disaster with multi-plats.

What's problematic is that none of the Xbox first party devs have managed to showcase any of that potential in a meaningful way, compared to PS3 which managed to revive it's reputation mainly on the back of first party titles doing so. Meanwhile XGS takes over half a generation just to release any over-funded tech demo, which came out to almost no fanfare and was forgotten in record time.

Aladdin vs Aladdin is the most famous case of this. Also games like Strider NES vs Strider Genesis. I won't delve into Bionic Commando and Ninja Gaiden Arcade vs NES. But yeah Genesis vs SNES vs TG16. Vastly different libraries. Even the games with the same name are sometimes different. Sometimes odd things would happen like a sequel would get exclusive to a competitor console. Assault Suit Leynos(Target Earth in the US). Only on Mega Drive/Genesis. Assault Suit Valken (Cybernator in the US) only on SFC/SNES. And the suicide scene was removed for the west until the Switch port. TG16-CD got an arcade port of The Ninja Warriors but SNES got the sequel. Also called Ninja Warriors or in Japan Ninja Warriors Again. (did get a remake on Switch as Ninja Saviors)

Sorry, a little ramble. I did like it when consoles were truly different. Another reason the Switch is awesome. Genesis had some great RPGs but it was mostly an action game machine from SEGA/Treasure/Masaya and more. Shmups. Mechs and sports. SNES thrived in RPGs. Platformers. Nintendo's IPs. They were great! PCE/TG16 thrived as more obscure but awesome shmups. VNs. Far East of Eden and Cosmic Fantasy RPGs which were popular in Japan.

Like i said this is very subjective when comparing 2 different engines with 2 different goals. In  your opinion naughty dogs games are more techically demanding then anything on 360 but it's really impossible to confirm this. I would say GTAV is more demanding then anything on those consoles of course it doesn't have the looks. also FORZA horzion looks stunning and makes gt5 look like crap. 

 It also not rocket science  that if it is  more powerful in real world performance it would eventually be able to show in some games, like it was a long gen where are these multiplaform games that actually take advantage of the power and prove it, not many big gap in thousands of games. so basically we are stuck with uncharted 3 being the show case and the reason for ps3 being more powerful in your opinion which is subjective and also can be based on the skill of the devloper. in  the end it's more powerful on paper but no developer could actually take advanatge in real world perfomance.

so i was using google to read about this subject more and this is the best answer 

In addition, these debates are always semantically impossible. Until there is a metric for quantifying how powerful a console is, every response will be subjective.

Anyone wanting to discuss how powerful a console is will need to first debate how we're going to measure it. Once consensus is reached and a unit of measure ratified (Flops? Ops? Shaded pixels per second? Bozomips? Pixels peek draw per GB per GB/s median average bandwidth attained 90% of operation per GB/s minimum bottleneck bus width per instruction per clock per processor core per pixels drawn on screen in interquartile number of games?), then we can measure these consoles and sort them by this metric.

IMO it's best to use multiple games and if the games are winning then the console is better at running games which is all that really matters in the end. iI will never call a console that can't run most games better or higher rez more powerful.