The US said Mr McKinnon had assurances he would be tried in a federal court.
But defence lawyers said his human rights could be breached if he was sent to the US.
Mr McKinnon was remanded on bail until 10 May when District Judge Nicholas Evans will rule whether the extradition will go ahead.
Much of the hearing was taken up with argument over whether Mr McKinnon would be subject to Military Order Number One - a legal procedure which enables the president to specify that suspects can be detained indefinitely.
Mark Summers, representing the US government, said there was no precedent to suggest the US would breach its promises, and the court should take on "faith" the undertaking.
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