Teddy Roosevelt, fond of saying "bully", used what we refer to as the Bully Pulpit - that is, he used his popularity, folksy style and good speaking skills to rally popular support for his causes and progressive reforms. This put pressure on Congress to follow suit, and helped other Progressives to get elected to Congress which also aided his programs.
Obama shares many of those same qualities and strengths with Teddy Roosevelt, although he is in a different economic situation. With the recent banking crisis and financial bailouts and scandals, the time is ripe in terms of public opinion to remorm these industries as a progressive would. He could use Roosevelt's bully pulpit style to achieve his agenda more easily and completely.
Theodore Roosevelt is best known for a very aggressive foreign policy (the "Big Stick" policy). I would argue that this type of foreign policy is no longer possible in today's world.
In Roosevelt's time, the United States, along with a few European powers and Japan, felt they had the right to divide the world into spheres of influence that they would each dominate. Roosevelt's foreign policy was generally aimed at making sure the US dominated its sphere of influence. He did this by interfering whenever he liked in the affairs of the weaker nations of the world.
I do not think this kind of foreign policy is possible anymore. Public opinion (in the US and abroad) has gone against this kind of attempt to explicitly dominate weaker countries. If Obama tried it, he would fail because the world will no longer accept that kind of policy.
If I understand the question correctly, the purpose would be to engage in an authentic and legitimate comparison between both presidents, as opposed to making personalized judgments that resemble talking points from a political party memorandum. There can be several approaches to this question. There are some distinct problems in presidents "attempting" to be like their predecessors. Part of this reason might be due to the fact that there are separate and distinct conditions that face different presidents. For example, when President Roosevelt took office, there was little in way of media criticism of the President, in comparison to now. President Roosevelt's private affairs and his health were concealed from the public as everyone understood what is at stake. In the modern setting, there is little way one can conceive of the media, in all of its different forms, keeping realities of this magnitude silent. The economic challenges facing both presidents bear some similarity, in that a different and new role of government is needed. FDR saw government as a tool to help people, and President Obama sees it, to a lesser extent, in much of the same way. Some could argue with what President Obama is attempting to undertake in health care, he is mirroring much of President Roosevelt.
Obama could learn to be more patriotic and love his own country that he is being allowed to preside over. He should also learn what it is to fight first hand for America instead of taking office from only being a a community service organizer or whatever he was. Yes, he should be more like Roosevelt.