XCOM is an excellent game, but I'd argue that it fails as a remake. Despite the superficial similarities, it's a completely different game. It owes quite a lot to modern boardgames of the past 10-15 years, and not so much to the trend of highly detailed, simulationist computer games in the early 90s which had X-COM as one of its crown jewels.
Both the combat and the strategic phases of XCOM are very boardgamey in their own way. And it works, it's great fun. But in terms of game design, it's about as far away from X-COM as you can get while still retaining the same basic components.
What do you think are the biggest changes? To be honest I was too young to fully appreciate the original xcom when it came out, so I don't remember that many big differences. I think the update in soldiers levelling up is a big one. Very different approach to bases/hangars is another. Engineers/scientists as resources are newish. But that's in the planning part - what's so different in the combat phase apart from abilities? I think the areas were larger and the AI did more things than "attack" and "flee", but I'm not 100% sure. I don't remember enemy units being dropped onto the battlefield as the mission progressed either.
Both the combat and the strategic phases of XCOM are very boardgamey in their own way. And it works, it's great fun. But in terms of game design, it's about as far away from X-COM as you can get while still retaining the same basic components.