Miliband is a ultimately a politician of the establishment and was merely a sort of Blair-lite as leader.
Media and media organisations tend to be a bit of an echo chamber. The Tory media, which is the majority of the UK media, will always attack anybody who is the Labour leader, bar Blair, and thus Miliband did take a pounding in the right-wing media.
But there is a certain spectrum of opinion that is considered as valid by the media in general and the media sees Corbyn as lying outside that whereas Miliband ultimately lay inside it. Nominally "left-wing" press also adhere to this spectrum of legitimacy. This is despite Corbyn's policies being pretty mainstream social democratic in a traditional sense.
This spectrum of legitimacy has been established over decades by media ownership taking the media in general in right-wing direction, political results and future expectations of them, and constant reinforcement within the media bubble through media-savvy pro-business think tanks, ownership which is sympathetic to advertising interests, and content which is advertorial in nature. Miliband was willing to work within that kind of system whereas Corbyn is seen as hostile to it.
"Consensus" brooks no disagreement and woe betide those who disagree. We've seen it regularly in this country.
In the US Trump lies outside that spectrum of legitimacy too, although for very different reasons than Corbyn, and I'd argue both the Trump and Brexit campaigns were/are classic insider/establishment campaigns posing as anti-establishment for strategic gain because they realise the political landscape has changed in terms of hostility to "establishment politicians".
The Israel lobby is a huge influence on media and politics in general in the UK. Because Corbyn has always been anti-Israeli government policy, this is a convenient avenue of attack against him in the media in a way it couldn't be with Miliband.
Corbyn is portrayed as having dodgy friends when the Tories have far, far dodgier ones such as the Saudi regime and Islamists in Syria, as well as being slavishly pro-Israeli government policy and completely beholden to financial interests, but this is nearly always conveniently overlooked.