Apple is trying to get an additional $380 million (£237 million) from Samsung on top of the $600 million (£375 million) the firm has already paid it in an ongoing patent infringement case.
Samsung is arguing to the jury that it should have to pay just $52 million (£32.5 million). The judge had cut around $450 million (£280 million) of the original award.
The arguments were presented by Apple lawyer Harold McElhinny and Samsung lawyer Bill Price during opening statements at a retrial in northern California.
A new eight person jury is now charged with choosing whose amount should be paid. Samsung was found guilty of infringing on five Apple patents related to the iPhone's design and functionality.
"We will hear a lot from Samsung, saying no one would have purchased Apple products," McElhinny said. "But in its heart, Samsung knew it was a two-horse race."
He also pointed out an internal Samsung document as "conclusive evidence Apple lost sales because of Samsung".
In response, Samsung's Price, argued "Apple is asking for more money than it's entitled to."
Price said that, although Samsung did infringe on some patents, such as bounce-back screens, this is not the only reason people buy Samsung smartphones - they head to the Korean firm for bigger screens, removable batteries and 4G LTE service, among other features.
Apple's $380 million (£237 million) figure is based on lost profits of around $114 million (£72 million), Samsung's earnings of about $231 million (£144 million) from the infringement, plus royalties of $35 million (£22 million).
Apple reckons it would have shifted 360,000 devices if Samsung had not released rivals that infringed on its patents. McElhinny predicts Samsung sold 10.7 million infringing devices, providing $3.5 billion (£2.2 billion) in revenue.
"In a fair fight, that money should have gone to Apple," McElhinny said.
Conversely, Price, said Samsung believes Apple should not get any money for lost profits, just $52.7 million (£33 million) for Samsung's profits, and a royalty fee of just $28,452 (£17,741.5) due to limitations of the patents.
The Apple vs Samsung patent battle royale began in April 2011 when Apple filed a suit against Samsung accusing the firm of copying the design and user interface of the iPhone 3GS.
Samsung quickly countersued two months later alleging that Apple had infringed on a number of patents concerned with technology. The two have since been embroiled in over 50 lawsuits.