2 of key things you should consider before making a decision between these 2 vacuum cleaners:
The first one is the power source, the Shark Rocket is corded while the Dyson DC44 is battery powered. The DC44 battery life is under 20 minutes and it takes about 5 hours to fully charge up, this is a little hard to take for some people.
The second one is the cost, Dyson DC44 is over $100 more expensive than the Shark Rocket when we post this comparison table.

Shark Rocket vs DC44 Animal Cordless Vacuum

	Shark Rocket	Dyson DC44 Animal Bagless Vacuum Cleaner
Design	Stick / Handheld	Stick / Handheld
Bagged or Bagless	Bagless	Bagless
Dirt Bin Capacity	0.472 dry quarts	0.09 gallons
Power Source	Corded	Battery Powered, Nickel manganese cobalt battery
Power	120V., 60Hz, 500 Watts, 4.2 Amps	22.2 volts
Cord Length	Depending on the version you purchased, HV300 = 27', HV301 = 30', HV302 = 30', HV302Q = 30', HV300W = 32'	NA
Battery Run Time	NA	20 minutes at normal mode or 8 minutes on boost mode
Charge Time	NA	about 5 hours
Motorized Brushroll	Yes	Yes
Dual Speeds	2 brushroll speeds slow speed for cleaning bare floors and delicate area rugs, high speed for cleaning carpets.	dual power modes 28 airwatts at normal mode or 65 airwatts in boost mode
Can the brush bar be turned off to vacuum hard surface floor?	No	No
Weight	under 8 pounds	5.07 Pounds
Height Adjustment	Automatic Adjust, no manual setting	no manual setting
Nozzle Width	10.5"	8.25"
Extension Wand	Yes	Yes
Washable Filters	Yes	Yes
HEPA Filter	No	No
Headlights	No	No
Included Tools	Dusting Brush, Pet Hair Tool, Crevice Tool, Dust Away Attachment Kit, optional Car Detail Kit	Combination Tool, Crevice Tool, Mini Motorized Tool
Wall Mount	Yes	Yes
Color	Orange and Blue	Purple and Grey
Price
Warranty	5 year limited warranty	2 year limited warranty
Manual	Shark Rocket Manual Download Link from Official Site	download user guide from dyson.com

These are 2 bagless stick vacuum cleaners that can also be converted into a handheld vacuum cleaner.
One of the main differences between them is the power source. The Shark Rocket is corded while the Dyson DC59 is cordless. The corded one limits the area you can reach so you might have to change outlets to clean your home while the battery powered one have a drawback on running time. And the cost is another thing you should consider, DC59 is about $150-$200 more expensive than the Shark Rocket at this moment.

Shark Rocket vs DC59 Animal

	Shark Rocket	Dyson DC59 Animal Bagless Vacuum Cleaner
Design	Stick, Handheld 2 in 1	Stick, Handheld 2 in 1
Bagged or Bagless	Bagless	Bagless
Dust Cup Capacity	0.472 dry quarts	0.12 gallons
Power Source	Corded	Cordless, Battery Driven
Power	120V., 60Hz, 500 Watts, 4.2 Amps	350w motor
Cord Length	Depending on the version you purchased, HV300 = 27', HV301 = 30', HV302 = 30', HV302Q = 30', HV300W = 32'	NA
Battery Run Time	NA	26 minutes of cleaning time on standard mode, 6 minutes on boost mode
Charge Time	NA	about 3 hours
Motorized Brushroll	Yes	Yes
Dual Speeds	2 brushroll speeds slow speed for cleaning bare floors and delicate area rugs, high speed for cleaning carpets.	2 suction modes 28 airwatts at Standard Power or 100 airwatts in Boost mode
Weight	under 8 pounds	4.6 lbs
Height Adjustment	Automatic, no manual setting	no manual setting
Nozzle Width	10.5"	about 10"
Washable Filters	Yes	Yes
Wall Mount	Yes	Yes
Headlights	No	No
Included Tools	Dusting Brush, Pet Hair Tool, Crevice Tool, Dust Away Attachment Kit, optional Car Detail Kit	Mini motorized tool Combination tool Crevice tool
Color	Orange and Blue	Purple
Price
Manual	Shark Rocket Manual Download Link from Official Site
Warranty	5 year	2 year

Want to share your opinion on these 2 Shark and Dyson vacuum cleaners? Please comment below.