Tycoons from both countries are not shy of a fight. The fallout from the tussle between Russia's Roman Abramovich and Kolomoisky, where the Russian has accused the Ukrainian of scamming to the tune of billions of dollars, is one notable example. Kolomoisky has also had a very public battle with Ukrainian pipeline magnate Victor Pinchuk. Pinchuk is the son-in-law of ex-President Leonid Kuchma.
Putin personally commented on the Abramovich row Tuesday, saying Kolomoisky had "cheated" Abramovich.
(Read more: What Russian TV is saying about Crimea)
"Ukrainian politicians are often political businessmen. You get into politics to gain or protect assets," David Dalton, economist for Central and Eastern Europe at the Economist Intelligence Unit, told CNBC.
"The difference with Russia is that in Russia, the state is much stronger and there is more to go around."
(Read more: Why Crimea matters)
After its recent turbulent political history, Ukraine does not have the same history of a strong central government as Russia.
The appointment of Kolomoisky, who is Jewish, is an important tool against Russian claims that the new Ukrainian administration is "fascist" or anti-Semitic, as well as a way of keeping him on side for Ukraine's new government.
Yet appointing prominent figures from Ukraine's past may not help achieve the new regime's stated objectives of reforming its economic system to increase productivity, innovation and fairness.
"The protests began as pro-EU, then became anti-government, then anti the economic system. The basic aim is to split business and politics," Dalton pointed out.
- By CNBC's Catherine Boyle. Twitter: @cboylecnbc.