Yes, I've still been thinking about them.
I got to revisit both on the big screen in 2010, when Cort Webber and Bobby Roberts showed them as midnight movies at the Bagdad Theater*, and I'd watched each multiple times before. They're both disaster films very much of their mid-Nineties time, and parts of each film are dated (JP's sudden sexism lecture, ID4's hinging on the alien tech being Mac-compatible), but I look back with more fondness on the Roland Emmerich-Dean Devlin work than the Steven Spielberg work.
To me, ID4 "owns" its disaster-film-ness more than Jurassic Park, which seemed to try harder to be Almost Profound And Making A Statement About The Way We Live Now (technological progress in our modern, confusing world MUST BE DONE CAREFULLY) when, come on, we wanted to watch rampaging dinosaurs. Michael Crichton's original book, which I liked enough to read a couple of times, of course has more room to make its philosophical statements without them feeling shoehorned-in. The book even gives the dinosaurs chances to be poetic; certainly the film has poetic moments, but I'm thinking of the novel's scene where survivors find dinosaurs massed on the island shore and think They want to migrate. But I found the film version's attempts at being profound to be a little silly when they're in service of (as Peter David pointed out back then) a "Murphy's Law" plot.
Actor-related quibble, too: Jurassic Park came out at a time when no filmmaker other than Spike Lee seemed to know how to use Samuel L. Jackson. He gives a fun performance as one of the computer techs, but it's a shadow of what Jackson was and is capable of. At the time he was starring in films like Amos & Andrew, which also didn't showcase his talents particularly well. (Yes, there was a time before Pulp Fiction.)
So after all that, the sequels to Jurassic Park seemed, to me, obligatory instead of worth my time. I waited to see 1997's The Lost World edited for television, and didn't feel I'd missed much by waiting; and I had no desire to watch 2001's Jurassic Park III (my fondness for director Joe Johnston aside) or last year's Jurassic World (my fondness for Jimmy Buffett aside).
Meanwhile, yes, Independence Day is often broad and silly. I admit that almost every time I bring it up. But I still like its unabashed bigness, making it clear this is a global threat that needs a global response. It feels less cynical than Jurassic Park, less calculated, and, truly, less lily-white: ID4's cast is just more interestingly eclectic (if sometimes seeming like they're acting in different films, and mostly not at the acting caliber of JP's cast). More and more, I find disaster films kind of wear me out and make me a little sad, but somehow this doesn't happen when I watch this one. The humor of several characters, like Will Smith's, helps.
Maybe it's that Jurassic Park is about us getting things wrong, while Independence Day is about us getting things right. Maybe I respond more to that. I do know I'm currently more interested in next summer's Independence Day: Resurgence than whatever the next Jurassic Park is going to be.
* I wrote about each that year: Independence Day in July, Jurassic Park in August.