Biiig difference there.  Jugular vein laceration, especially external jugular vein, could be compressed externally to prevent "bleeding out" (though depending on the size of the wound, there might need to be a formal repair done).  Heck, a neck surgeon might nick the jugular vein in surgery and it might take 24hr or so to determine that there is a problem.

A complete unilateral carotid artery transection would be scary (and messy) as all get up, but with optimal first aid should (might) be survivable.  Interestingly, a small nick of the carotid artery spurts a further distance than a complete transection.  A complete bilateral carotid artery transection wound cause a loss of consciousness very quickly (<10 seconds) and a "bleed out" in 30-60 seconds.  That is to day, experimentally, the spurting loss of blood drops away dramatically at about that time.  There is about 400mL per minute flow through each carotid artery.  Total human blood volume is about 5000mL, however haemorrhagic shock passes the point of no return at somewhere about 1500mL total loss (2000mL with optimal resuscitation).

Fun times.

Cheers,

KenB