We will compare Shark NV356E and UV420, and list some main difference between them to help you buy the right one for your home vacuuming.
NV356E vs UV420
images from manufacturer
Lift Away Canister
The Lift Away Canister Design on the NV356E is one major feature that makes the difference between Shark NV356E and UV420.
The NV356E Portable Lift Away Canister allows you to carry the Lift Away (without the floor nozzle) with you to clean around your house, this is convenient while cleaning those hard to reach spots, stairs, vehicle, etc.
Here is an image taken from the NV356E manual to make the above text more clear.

The UV420 is an upright pro model but not a lift-away model, it does not allow you to detach the canister from the floor nozzle to do cleaning jobs like the NV356E. For cleaning areas like stairs, it has the longer hose to help you do that job.
Included Tools
The NV356E comes with a hard floor tool which is called Dust Away Hard Floor Attachment and 2 reusable microfiber pads to remove dust and particles from hard floors.
On top of that, the NV356E also comes with 2 crevice tools: a short one and a long one that has a length of 24 inches, a Dusting Brush, and a Pet Power Brush.

While the UV420 has NO Dust Away bare floor tools, but comes with 2 crevice tools: one short and one long that has a length of 16 inches, a Dusting Brush, and a Pet Power Brush.
Besides the above mentioned tools, the NV356E has an extension wand while the UV420 comes with 2 cleaning wands including one with handle and one without handle. Here is an image taken from the UV420 manual:

Handle
The handle on the NV356E is removable, you can separate the handle from the vacuum body, and attach desired tools for above floor cleaning or portable cleaning.
While the UV420 has a fixed handle that is not detachable.
Weight
The UV420 is a bit heavier and bulkier.
Hose Length
The UV420 has a longer hose than the NV356E.
Dust Cup Capacity
The UV420 has a larger dust cup that holds more.
Similarities:
These 2 Shark upright vacuum cleaners also have some similarities, such as the
Anti-Allergen Complete Seal Technology and HEPA filtration;
pivoting head for easy steering;
carpet/rug cleaning mode or suction only mode for cleaning bare floor;
self height adjustment without manual setting.
You can download the UV420 manual and NV356E owner’s guide to learn more details about them before buying:
NV356E Manual: http://www.sharkclean.com/include/pdf/manual-NV356E.pdf
UV402 Manual: http://www.sharkclean.com/manual/UV420_26_IB_E_120810_3.pdf
Overall, the NV356E with Lift Away canister and Hard Floor Attachment is more versatile and portable (it would be better if it had a shoulder strap), while the UV420 gives you a Longer Hose to reach further and a larger Dust Cup to hold more dust and debris so you spend less time to clean.