The first thing that should be kept in mind is that in the present duumvirate, Medvedev and Putin are not rivals. They are members of the same team and have worked together for years. Thus, the most logical beginning, rather than looking for disagreements, is to attempt to see how they work in a complementary fashion.
When Putin became president all indicators in Russia were negative (as a reminder see “Russia is Finished” from the Atlantic Monthly of 2001). His early speeches show that he was seriously concerned that Russia might literally fall apart. I believe that he had four aims when he began: to reverse Russia’s economic decline; to halt fissiparous tendencies; to improve Russia’s standing in the world, to institute what he called “rule of law” but what might better be termed “rule of rules”. He can – and has – claimed real progress in the first three but has admitted to little success in the fourth. Indeed he once said that corruption had been his greatest failure. His style of governance was very centralising, not surprisingly given his fears about breakup. It can be argued that all this worked reasonably well for most of his eight years.
Medvedev became president in a less desperate time (although the unexpected international financial crisis has taken some of the shine off the economy). Although he worked with Putin in the bad years, he presumably is not so concerned with the possibility of sudden collapse. He can, therefore, be more relaxed.
Another difference is that during Putin’s time (and Yeltsin’s for that matter) prime ministers were, with the notable exception of Yevgeniy Primakov, creatures of the president. All decisions came to the president’s desk (something Putin once publically complained about) and others obeyed (or, quite often, ignored) presidential orders. Under the present duumvirate, Russia now has a prime minister of real status. This permits a different division of labour. We indeed see Putin working at the “first minister” details and Medvedev discussing the larger “presidential” policy issues. This is not the only possible division of labour but it appears to be how this one is shaping up. Indeed, for one of the few times in its history, Russia has a degree of pluralism of power. This could lead to trouble, as dual power has before, but so far the two are cooperating. The common assumption that Putin still rules Russia is too facile: there can be no question that he could have amended the constitution and been elected for a third term. The astute analyst must seek to understand why he chose the course that he did.
Medvedev has his sphere and Putin has his. It is clear that Medvedev’s sphere is “rule of law”, in the widest sense, and encouraging the modernisation of Russia (witness his recent remarks on “the information society”). It is also probable that he seeks to loosen some of the centralisation (over-centralisation to my mind) of the Putin period. This should not be seen as disagreement with Putin, neither should it be seen as tension between the two, but rather what is appropriate for Russia’s circumstances today.
Finally, one should reflect on the fact that Russia has had two presidents in a row who were greatly affected by Anatoliy Sobchak. There should be less obsession, to my mind, with Putin’s KGB background and more consideration of the “Sobchak factor”.