[Jayd2014]

"As such, they stated (against the laws of Islam) that non-Arab converts to Islam still need to pay the same amount as they were paying before they embraced Islam. Naturally, this led to a lot of resentment amongst the new non-Arab Muslims who would later support the Abbasid rebellion against the Umayyads."

First the Jizya was not a Tax payed because they weren't Muslims. It was payed for everyone who didn't participate in Islamic military. Think of it like a Latino living in the US and paying a fee (passport fees, green card fees..etc) for not participating in US military. Non-Muslim benefited from the same as Muslims in terms of public social help. Secondly, Zakat can be sometimes higher than the Tax paid by non-Muslims. Depending on how much you own.

[nraf]

The jizya was payable by non-Muslims dhimmis living in an Islamic state. I don't know of any requirements that had to do with participating in the military, as there were non-Muslims citizens who fought alongside the Muslims (e.g. Christians battling in the Ottoman armies). The only thing I've heard is that the jizya is to refunded if the Muslims fail to defend the non-Muslims paying jizya if they're attacked. Not sure how accurate that is though.