I think they're essentially equally nefarious because in the end it's all about power and money. It's just that russia is a young "democracy" with corrupted institutions and an authorian leader who's been in power for almost 20 years which makes their actions around the globe seem worse. Whereas the US is an established republic with working institutions and the leadership (the presidency, not congress or senate) changes every 4th or 8th year. This makes it seem as if though the US ambitions on the global arena differ between each president and ofcourse this is partly true. One President may want to reinvigorate relations with another nation (i.e. obama with cuba and iran) whereas one wants to go tough etc. but I think that the core ambitions are always intact regardless of who is president. For example to remain like you called it "the world police", imposing military or economic (sanctions) action against anyone who dare go against them economically, militarily or politically. What I'm trying to say is that they're both essentially working for the same goals, power and influence, just that they do it in different ways and that the US perhaps make it look cleaner.
In order to find what differs them I think we have to look at what positive things they both do rather than the bad things we've talked about. The huge influence the US has around the world have enabled them to also do good, a lot of good actually, especially compared to a country like Russia. The US (just like Sweden) spend quite a lot of money on foreign aid, assisting poorer countries with money, medicine, food and other supplies. If I remeber correctly a majority of soldiers and other personel working under UN banner in conflict or disaster ridden countries are also American. US companies also create a lot of job opportunities around the globe. Also, a thing that I've come to realise which is a bit off-topic but still interesting is that many american products are very often taken for granted by people across the globe. I personally have met many people who for some reason hate everything about the US yet they sit there with their american phones, clothes and watch american television.