Ehrmahgerd, prelerding!
I find that getting into really old games these days can be rather hard, even if you do play other really old games, or DF, or roguelikes. It might just be me running out patience at life though.
What other people have said is usually spot on, but they haven't put focus on the strategic side of it. It's not just a series of detached missions, and there's more than just some guys surviving until the next mission and others not. The strategic side did have you thinking a bunch, and gave you a constant sense of progression. You have some fairly meaningful decisions you need to make, such as what to research first: more advanced weapons or medkits? Some base defenses (since you're bound to have your base attacked soon) or start researching that new craft that will take more rookies to the slaughter? It takes a long time to research everything and build the craft... should you build a new base? Where? For what purpose? Should you get more engineers or more scientists?
Put simply, the game is constantly throwing meaningful decisions at you, although not in an explicit manner. This is true of both the tactical and strategic part. The new one, I think, makes it easier for you to see and make those decisions by making them explicit. That simplifies the whole process, so perhaps there won't be quite as much choice, but like people have mentioned, the original game could get bogged down with technicalities that weren't really interesting. I'm hoping it's not "linear" literally despite the simplifications. I don't think it will be, since all the devs still seem to be playing. Linearity really doesn't lend itself to that!
Also, the first X-com is piss-cheap, so there's barely any cost to trying it