The Rami one's just don't capture the way momentum works. It's just him floating about NYC, he doesn't fall fast enough at all in those films. He floats over to the Murican' flag to swing off.
They relied heavily on close up shots with a speeding background too in the spidey films, in the ASM series they had much more flexibility with the shots they could have.
Look at Daltonio's GIF for example. Look at the web recoil, and act natural (not rigid), look at how spider-man, after shooting out his web with his left arm, starts drifting off to the righ as his weight begins to favour one side. Look at how he falls faster the lower he goes.
The variation in height, in swings, the way he'll shoot out a web and sorta "Mini-Climb" it during TASM2, all wonderfull. I'm sure Raimi wanted to do stuff like that but the tech didn't allow it.
To be frank if you're calling CGI from a decade old better than the current stuff then there might be some Tobey coloured glasses in play.
Spider-Man 1 wins hands down for the best monologue before final swing tho.
"Whatever life holds in store for me, I will never forget these words: "With great power comes great responsibility." This is my gift, my curse. Who am I? I'm Spiderman."
Best dialogue out of any spidey film.
Actually Spider-Man 1 had some amazing dialogue, I'm going through some quotes now.
"Here's the real truth. There are eight million people in this city. And those teeming masses exist for the sole purpose of lifting the few exceptional people onto their shoulders. You and me… We're exceptional."
And then Spider-Man 2.
"Too few characters out there, flying around like that, saving old girls like me. And Lord knows, kids like Henry need a hero. Courageous, self-sacrificing people. Setting examples for all of us. Everybody loves a hero. People line up for them, cheer them, scream their names. And years later, they'll tell how they stood in the rain for hours just to get a glimpse of the one who taught them how to hold on a second longer. I believe there's a hero in all of us, that keeps us honest, gives us strength, makes us noble, and finally allows us to die with pride, even though sometimes we have to be steady, and give up the thing we want the most. Even our dreams…"
I know it's a tad off topic, but man, the ASM series had nothing on the SM serie's dialogue.
Seriously though the effects look better and that's to be expected, the OT is a decade old and it's not going to look better than the new stuff. That's really just the reality how how quickly tech develops this days, especially if we're comparing CGI. (Practical vs CGI still has merits, but if its straight CGI comparison and you're comparing movies from different decades, then logic should direct you to the result)