Bradford only has 1 year remaining on his contract, so by 'restructure', i'm assuming you mean 'extend' ? By extending his contract the Rams could reduce Bradford's 2015 CAP hit, but there remains the injury risk going forward.
If we trade Bradford, his new team will take over his salary and the Rams would only assume his 'dead money' CAP hit of $3.5mil. If we were to cut Bradford, we could re-sign him for a smaller salary, but we still take the 'dead money' hit to the CAP. Also, if cut, he can negotiate with any team in the NFL, so that gets risky if we hope to re-sign him.