I'm watching Dante's Peak (1997), a volcano flick starring Pierce Brosnan.
The colours are just so wonderful -- it's like being outside in real nature.
Whereas with modern movies things seem really washed out. The filming is crisp, and the composition is usually good, but it feels like you're living in a claustrophobic world. Modern movies feel a lot like living in 1984.
Is this the difference between film/digital? Or are people choosing different colour palates?
A lot of the colour grading happens in post production. But more specifically, if you watch a lot of the cinematography and digital editing channels on YouTube, they talk about how it's much easier to blend CGI effects into a scene if the colours are more washed out. It's why usually really dark scenes have the best uses of CGI, and rarely ever does it look good in a bright, well lit setting with vibrant colours, because it's difficult for CGI to match real life in many cases.
You'll note most "good" CGI shots in today's films take place at night, or poorly lit areas. A good example is the smile monster from Smile, or the snappy jaw things from Arcadia. In poorly lit areas with washed out colours you can usually integrate CGI better and fool the viewer into thinking it looks more integrated.
Likewise, for films without a lot of CGI that are just washed out, it fits in with what some of the other comments here mentioned about the directors thinking they're artists and trying to depict what they think is "realistic", or "gritty", when in reality it's just washed out and boring.