I wouldn't call the gameplay in the first Mass Effect dated, so much as I would call it different. And, well, flawed, I guess. The main story is a lot better than in the sequel, though.
As long as you don't overindulge on sidequests and don't mind emptying your inventory every couple of hours, it's a lot of fun.
Eh, they're both decent enough platformers, but the main reason to play them is the imaginative places you visit and the dark twists on the classic characters (more so in the first game, as the second game seems to focus on more obscure characters).
It's been over a decade since I played the first game, but I don't remember the levels dragging on as much as they did in the sequel.
If you can live with average gameplay because you think the other stuff makes up for it, then they're worth playing.