Oh man. IW defence force here. I wish you hadn't asked this question because now I feel inclined to have to answer it and I really don't feel like having to get into it with anyone... I could write books on what IW does right and what IW does wrong. Invisible War is pretty much universally reviled by anyone who has a red name on this forum, but I've played through it a few times and really enjoyed it, warts and all.
Go into it with an open mind and preferably without reading too many opinions on either side. Some of its faults were of a technical nature, many of which are irrelevant now because it runs much better on modern hardware, the biggest issue - and the one that can never be fixed - is that the map sizes are tiny so getting through the hubs can become a pain in the ass. Other than that, it does some things kind of differently than DX and HR, or at least the focus is different. HR is literally (and sometimes quite disappointingly) a carbon copy of DX but with modern conveniences. IW is a more... social game I guess? It revolves more around your interactions with the people in it's world and the way you react to them, it's more emergent than DX's smoke and mirrors in that respect. You can't play IW like DX in that if you try to explore every nook and cranny and try to please everyone all the time (you'll understand what I mean), you kind of break the game's narrative. The best way to experience your trip through it's story, and this probably sounds silly, is to just follow your heart. It's short, play it again if you have OCD.
It's an interesting yet misunderstood experiment in emergent gameplay that succeeds and fails on many different levels. The only things off the top of my head that come close to exploring what Invisible War did is the Witcher games and Alpha Protocol. Not too many devs are up to the challenge, apparently.
One thing's for sure though, if HR was IW, some of the things we're taking for granted in HR in 2011 (recharging health, third person stealth etc) would have rendered the series as completely dead to DX fans in 2004 as IW did. Eidos were smart for putting it on ice for a few years.