EDIT:
Both Obama and Roosevelt had similar opponents. As both of these men pushed to spend and stimulate the economy as well as creating social benefits to help the people, their critics feel like it is a waste. They feel that spending will just be a waste of taxpayer money that could be spent in better places. To them, social benefits are a waste since it should be a free economy with every man for himself. Roosevelt openly stated that he despised Big Business and that they were evil for trying to suck the last dollar out of its citizens. Obama has been compared to him heavily in this fact since he wants to create a higher tax for richer people and cutting tax breaks large businesses receive. Obama has stated that Big Business shouldn't need such a helping hand, they are not people. The tax breaks we focus on giving them could be better spent on helping the less privileged people of America.
I think they are very similar. They both seem to have a left wing ideology and want to help the average citizen. They feel like it is their duty to make sure everyone has an equal opportunity. In today's inauguration ceremony, Obama stated that he hoped that no citizen should have the burden of a financial emergency burdening them and that the government should help them because it is their duty to look out for their citizens. Sounds like an awful lot like Roosevelt pushing for unemployment insurance because of the strain it could put on a family. (Obama and Roosevelt were also sworn in 4 times, the most any president has ever been.)
Resources used:
http://www.britannica.com/blogs/2010/12/barack-obama-and-fdr-a-misguided-if-inevitable-comparison/
http://www.esquire.com/blogs/politics/are-you-better-off-obama-vs-fdr-12374597
http://www.cbc.ca/news/world/story/2013/01/21/obama-inauguration-speech-transcript.html