The relationship between sympathetic/parasympathetic nervous systems and blood flow regulation really depends on the target organ/gland in question. The best way to approach this problem is to understand what each branch does:
Sympathetic (SNS)--> "fight or flight", so you'd expect to be more active and alert
Parasympathetic (PSNS) --> "rest and digest", so you'd expect to be more laid back and relaxed
So in a SNS response, you really wouldn't want to be staying relaxed and eating happily, since that's activated in the clear sign of danger. This means much of your blood flow would be focused on regions that would help you defend yourself and escape, not on digestion. Likewise, in a PSNS response, you wouldn't be stressed but instead relaxed. You will rather spend the time eating and enjoying leisure, so blood flow would be focused away from movement and more on digestion and related processes.
Vasoconstriction/vasodilation refers to the fluid dynamics of blood flow:
Constrict --> get smaller --> more resistance to flow (because blood can't move easily if it's congested) --> less gas/nutrient/heat exchange
Dilate --> get larger --> less resistance to flow (larger regions allow for blood to move easily) --> more gas/nutrient/heat exchange
Vasoconstriction restricts blood flow to certain regions in order to minimize gas/nutrient exchange to nonessential regions during a specific response. Vasodilation does the opposite: maximize gas/nutrient exchange to critical regions. Under SNS, vasodilation occurs in skeletal muscle because it provides much more energy and oxygen to escape from danger. You don't want to waste this energy/oxygen in your digestive system if you want to escape, so vasoconstriction occurs in this region. As you can expect, the opposite happens under PSNS response.
Heat exchange across the blood vessels follows the same pattern as gas/nutrient exchange. Vasoconstriction conserves heat and keeps your body warm. Vasodilation reduces heat and keeps your body cool.
