The original one was about a man who had his memory wiped and a new one implanted. I'm not exactly sure why they would do that, but if they just killed the guy, there wouldn't be any story. Anyway, his day job is boring him to the max and he wants a little excitement in his life so he goes to a place called Recall. This is a place where they give you some kind of canned memory at a much more affordable price than going on a vacation, plus you can choose something exotic like go to Mars.
Now the remake is a lot the same. The big difference is that Mars might be a possible memory destination but that's all. In this one, it's not a Mars colony they're trying to save, nor is it the lack of air they need to rescue them from. In this version we've cut travel from London to Australia to fifteen minutes by going through the core and Australia is the colony in need of rescuing. In this version, Australia is the slave labor force and the powers that be would like to replace all that man power with robot power.
With the significant story-line change, they should have given it the chance it deserved by giving the movie its own title, character names, and dialogue. Instead, they tried to follow the same line of events, sticking in identical dialogue here and there. Now, if you'd never seen the first one, you wouldn't know the difference; it's just fine all by itself. Full of action, adventure, and even love, not to mention the awesome future world setting. It's great. But if you're at all familiar with the first edition... Well, it's just kind of sad that so many things are identical.