Shark NV370 vs NV360
images from manufacturer

The major difference between Shark NV360 and NV370 is the type of brushroll they are equipped with.
The Shark Navigator Lift Away Deluxe Upright Vacuum NV360 has a Standard Brush Roll while the Shark Navigator Lift-Away Pro Special Edition Upright Vacuum NV370 features the Premium Brush Roll that has the Shark’s Gentle Deep Clean Technology which provides a gentle but deep clean.
Furthermore, the Shark NV370 is approved by The Carpet and Rug Institute (CRI) for use on all carpets and area rugs.

You can find it here:
http://www.carpet-rug.org/CRI-Testing-Programs/CRI-Seal-of-Approval-Program/Vacuums/Certified-Vacuums.aspx

Color
The Shark NV360 is blue while the NV370 is white with silver.

Cost
The NV370 is sligtly more expensive.

Included Tools
According to the NV360 manual, the NV360 includes a Crevice Tool, Dusting Brush, Pet Power Brush, and a Shark’s Patented Appliance Wand.
While the NV370 includes a Dust Away Hard Floor Attachment with 2 Microfiber Pads, 8″ Crevice Tool, 24″ Crevice Tool, Dusting Brush, Pet Power Brush.