Contrast and compare his positions on Bush's by the end of his presidency:
SOFA: Obama kept on Gates and Patreaus et. al. to execute the SOFA without any modifications.
Afghanistan: Obama tripled the number of troops, ultimately put Patreaus in charge, and has chosen to actually increase our commitment to a seriously corrupt administration in country.
Pakistan: Has increase drone attacks, as well as other attacks inside the country, frequently without the cooperation or approval of the Pakistani government at any level.
N. Korea: Has continued to execute the exact same policy of relying up China and offering assistance to Korea in exchange for restrictions on their programs.
Basically, you can pick almost any foreign policy, or military actions that Obama is doing and you'll find precious little difference from Bush. Even where you do find them, it is a matter of degree. It's not a different style, it is that Obama is actually successful. OBL is a great example.
The largest difference one might claim is on Iran. But FUNCTIONALLy the difference hasn't been that great. Bush resisted, despite the rhetoric, actually taking military action. He also restrained Israel from taking action either. Again, Obama has continued this, and one can make the case that he has been MORE successful in gaining the cooperation of the international a community, but that is making the case that he is doing it the same, just more successfully.
Basically, you're trying to make the case that core GOP foreign and military policies have been basically "correct" and they were just really bad at executing them. They had a disastrous detour into nation building which they ultimately abandoned by Bush's second term, and other than that they were just bad at executing "good" policy.