tl:dr Modern CGI isn't bad, it's great, the problem is the extreme overprocessing of the image and the "fix it in post" attitude that's making modern movies look more fake than JP
More natural looking on-set cinematography, less micromanagement in post. That's why JP has the edge.
Modern movies love to mess with all those dials and over process the image until even practical shots don't look real anymore. It's got to run through 12 different filters and have the graphics department comb through every frame to make 136 touchups.
It's not just about practical vs cgi like everyone likes to repeat forever. CG isnt the problem in itself. It's the amount of control modern effects afford the creators, and the overindulgence of control.
Modern filmmaking has so much control, and it's so easy, that every frame now gets a shitload of plastic surgury until it hardly resembles what was actually shot. Every shot must be flashy with perfect lighting and everything in perfect position with perfect color as intended by the director with absolutely nothing left untouched.
The problem is that real life doesn't look that contrived.
That's the real reason why movies look more fake now. It's not just CGI creatures replacing puppets and anamatronics. CGI can look absolutely real and the technology has improved dramatically since JP. The real problem is that cinematography today is more contrived looking than ever due excessive control and the attitude of "we'll fix it in post."
It's no longer enough to set up a good shot on a real set with the lighting you want and perform some standard adjustments to preference in post.
Now you've got to up the contrast, boost the color, brighten the main character's head a little bit, add a shadow on his left cheek, dull the red on his jacket, CGI his collar so it doesn't look messy, darken the distracting papers on the desk, replace the tree in the window, add light shafts to the window, tint the window green, run the shadows through a blue filter, run the highlights through an orange filter, add a gate in the background, sharpen the image, strengthen the rim light on the arm, move the arm slightly down, apply a little DNR, move the background character slightly to the left to fit better in the door frame, brighten the whites of their eyes, reapply artificial film grain. On to the next shot!
No wonder nothing looks fucking real anymore. Modern cinematography is contrived as shit. You could have a shot with no CG "characters" in it and it will still look fake. And those youtube videos you'll find that turn the contrast down and add a warm filter don't account for the other 1138 changes that have been made to the image already. It's not as simple as "color grading." It's the entire process that's fucked in these types of movies.
...but it doesn't hurt to try. It's interesting to see what JW might look like if they just laid off the fucking contrast a little.