As far as I know...
The difference is essentially a matter of where people get their jurisprudential (fiqhi) knowledge. Usoolis, which constitute the vast majority of Shi'a 12ers today, believe in a system called 'taqlid' wherein they derive their understanding of religious laws and rulings from 'marajae taqlid': mujtahideen (learned men fit to interpret religious law) who have passed through several levels of religious scholarship and are recognized to be the most learned and competent of the era's scholars. It should be noted that not all Usoolis are bound to follow the edicts of a specific scholar (see below). There are a lot of finer points worth reading up on in that respect.
According to al-islam.com, the fundamentals of taqlid are thus:
*"In matters of religious laws, apart from the ones clearly defined, or ones which are indisputable, a person must: *
- ** either be a Mujtahid (jurist)** himself, capable of inferring and deducing from the religious sources and evidence; **
- ** or if he is not a Mujtahid himself, he should follow one, i.e. he should act according to the verdicts (Fatwa) of the Mujtahid; **
- ** or if he is neither a Mujtahid nor a follower (Muqallid), he should act on such precaution which should assure him that he has fulfilled his religious obligation. For example, if some Mujtahids consider an act to be haraam, while others say that it is not, he should not perform that act. Similarly, if some Mujtahid consider an act to be obligatory (Wajib) while others consider it to be recommended (Mustahab), he should perform it. Therefore, it is obligatory upon those persons who are neither Mujtahids, nor able to act on precautionary measures (Ihtiyat), to follow a Mujtahid."**
Akbharis, on the other hand, don't believe in the application of reason (ijtihad) in religious rulings and don't believe in the authority of the marajae, and they rely solely on Qur'an, ahadith, and popular understanding to interpret religious law. The general Usooli argument against this methodology is that it's impossible not to use 'aql when considering ahadith contextually, and while Qur'an and ahadith may be more than sufficient to address many understood laws, there are more finite details in many religious matters that might not be addressed directly in religious canon, thus leaving a need for scholarly interpretation.
Sorry in advance for any discrepancies or errors!