There aren't many story differences in the two movies, up to a point they are pretty much the same. Towards the end of both movies Mr. Deeds makes a plea, to those that would listen, to follow their hearts and to act on what is right not what is popular. How they arrive at this point really is not that important, it's the message.
One of the main differences in the two is the time period, obviously. Mr. Deeds Goes to Town was a depression era film. That had a large bearing on the story it told. When Mr. Deeds realizes the responsibility he now had in the acquisition of this fortune, he sets out to make changes and not just minor ones. After being involved in a nearly violent exchange with a desperate out of work farmer, Mr. Deeds realizes that something has to be done about the joblessness. He proposes a plan that will give farms to nearly fifty thousand americans. A plan that is not appreciated by the people around him that want a piece of his pie. In the re-make, Adam Sandler's Deeds, is also concerned with the workers. It this story it is much more simplified, however. His intention is simply to keep the current workers of his uncle's company employed by stopping a proposed dissolving of the company. While it is nice to see that the plight of the worker is kept for the re-make, you can see just how much affairs of it's time affected the focus of the original. There was a crisis in our country and it was at the heart of Mr. Deeds Goes to Town. Given the state of our economy in recent time, if the new version had been made just a few years ago, instead of 2002, perhaps it would have had a similar focus.
While the original was a comedy, it didn't rely on it's jokes to carry it. It was about more than just the odd Mr. Deeds. This is one of the issues with the remake. It's mostly a comedy based on Adam Sandler's version of Mr. Deeds, than anything else. In my particular case it was filled with jokes that were not really funny. And when that is your focus, there's a problem. I'm not going to nit-pick the jokes in detail, comedy is a subjective thing and this was not good in my opinion. It was either a case of poor writing or the actors not being inspired.
Overall, the remake does hit all the points it would want to hit in retelling the original. It's lighthearted, funny (not for me, but it was for most I suppose) and has a good message about how we should treat each other. That's why I don't want to bash the modern version of Mr. Deeds, it had good intentions. So, which one was better? For me, with it's more heartfelt message and easy approach to the comedy, Mr. Deeds Goes to Town is the more enjoyable film. And should it have been remade? This is a case where i would say, no. The original is very good and worth watching. However, given people's tendency to avoid black and white films and our need to see contemporary actors in our films, I understand the need to remake it. While the remake doesn't quite have the emotional impact of the original, it still has a good message at it's core and I don't see any reason to deny that to modern viewers.