Arbitration is done by a company picked by Amazon, paid by Amazon, hoping to remain in business with Amazon, deciding about a conflict between Amazon and a random customer. In whose direction are they likely to err?

This is a late reply, but there are a couple big differences. The courts could create a class action, or join multiple claims. Avoiding a class action, where the individual claims are too expensive to be worth pursuing, but as a whole the wrongdoing is significant is one of the biggest driving forces in mandatory arbitration. But these don't apply to the linked case.

Discovery is more limited with arbitration, third party discovery is very limited, usually use witness statements instead of depositions. Arbitration almost never forms precedent, and arbitrators are not bound by case law/precedent. Decisions made by an arbitrator can only be appealed under more limited circumstances than if made by a judge. This means it is less likely a decision will be made based on the existing law. A court can grant interim relief, generally an arbitrator can not. A court will sanction parties that act in bad faith, in practice an arbitrator will not. A court judgement/sanction/relief can be enforceable in a way that an arbitrators finding would not be. This adds up to in practice making a successful claim more difficult for a wronged consumer

Arbitration is generally cheaper, limited discovery is cheaper. Not being limited to the same evidentiary rules and to respecting precedent allows the arbitrator to make more equitable decisions, that conflict with the law. Arbitration is faster.