From the UC perspective, there is no significant direct effect on the operating budget regardless of which budget is enacted. However, the assembly version provides for additional scholarship and Cal Grants funding so students have an interest in the final outcome. The hearing was not exactly a clash of the titans but you can hear testimony I extracted by the Chief Deputy Director of DOF and the Legislative Analyst (excerpt) explaining their differences at the link below.
The governor has a line-item veto and so could trim spending if the legislature enacts a budget he considers excessive. He could also veto the entire budget and throw the issue back to the legislature. In theory, the Democrats in the legislature could override such actions using their two-thirds supermajority. Whether all Dems would go along in that situation is uncertain. Minority Republicans now support the governor's cautious approach. The legislature must enact a budget by June 15 or forfeit pay for each day thereafter that they haven't done so. However, it is essentially up to the legislature to determine what defines an enacted budget. So there will surely be something by June 15 although there may be loose ends to tie up beyond that date.
You can hear the DOF and LAO testimony below:
The LAO prepared a summary of the three budget proposals for the hearing available at: