"Putin would have assassinated him.." means that Putin himself would kill him. "would have him assassinated" means Putin would arrange for some unspecified person or person to assassinate him. In the second version, "have" is not used as an auxiliary verb but as a causative verb. See this explanation; To Have Something Done - Arrangements - Have + object(s) + past participle This form is used to speak about something that you arrange to have done for you. This form is also known as the causative 'have' because it expresses something which someone else causes to happen. Examples: She had them delivered to her home. We had Jack promoted to director.

It is not Putin who would do "the dirty work" and assassinate him, he is giving the order for someone else to do it.

I just want to comment on this murder. It's a contract killing and direct challenge to Putin as Nemtsov was murdered right opposite the Kremlin.

And considering the fact that Nemtsov was murdered, why 'has been a fierce critic(...)' is put instead of 'had been a fierce critic'?