Vincent himself was only alive for about 20 minutes to see the first Confederate attack, which was admittedly the strongest, by five Confederate regiments (4th-5th Texas and 4th Alabama, followed closely by the 47th and 15th Alabama). It would have been bad news for the Federals to have driven off Vincent/Rice, allowing the Confederates to command the Taneytown Road, but Weed's brigade was close at hand to seal the breach, and the Regulars were not far behind, giving the Federals a decided advantage in numbers, until the arrival of the Sixth Corps before sunset.
Greene, on the other hand, contended his ground for ten hours over two days. For the first three hours (night of July 2) he was badly outnumbered, although he did receive only a little (but important) help from the First and Eleventh Corps. If he had been driven off, it might have been far worse for the Federal army if the Confederates had consolidated their position to command the Baltimore Pike, but the return of the rest of the Twelfth Corps before midnight sealed the breach on that flank.
All things considered, both situations were equally desperate and I find it difficult to choose between them. A big factor is the timing. The Confederate advantage on Culp's Hill was theoretically stronger because it could have been heavily reinforced, except the darkness limited the mobility of reinforcements. On the other flank, the arrival of the Union Sixth Corps made further gains by the Confederates very unlikely even if they had brought up reinforcements during the night - Pickett's division was out of the equation since it was too far away. For that reason alone I would consider the Culp's Hill breach to be more threatening to the Union army than the capture of Little Round Top on July 2.