The differences are considerable. It's best for you to identify them for yourself through a chronological description of the evolution from clone to stormtroopers, for while the origins of clones is common, the history very quickly branches out between Disney canon and Legends.
(tldr conclusion below)
Clone Origins & Characteristics (Lucasian Canon)
Jedi Master Sifo Dyas foresaw the coming of a galactic war, and - after his proposal was rejected by the Jedi Council - secretly contacted the Kaminoan cloners on his own to commission a new clone army for the Galactic Republic to fight the war with. Count Dooku - Darth Tyranus - subsequently killed Sifo Dyas and took over the project, whom the Kaminoans knowingly collaborated with despite knowing his true identity. Jango Fett was to be the original DNA template, and the clones were genetically modified for greater compliance to authority and superior innate abilities (reflexes, strength, speed etc.) compared to regular birth-born humans.
This is where the similarities between Disney canon and Legends end. In summary, subsequent differences between the two lie in the following points:
- How compliance to Order 66 is ensured
- What a Stormtrooper is and is not
- How the galaxy's main fighting force transits from being clones to stormtroopers
- Why stormtroopers are such bad combatants compared to Clone Wars veterans
Under the Sith Lords' instructions, the Kaminoans installed an inhibitor chip in all clones from infancy to ensure full compliance to Order 66. When the time comes to execute Order 66, the chip will override the clones' personal thoughts and emotions, ensuring blind obedience to the Order and an inability to resist it. It doesn't turn the clones into robots but rather change their mentality completely to perceive Jedi as enemies without question. After Order 66 was executed, it appears that control was released and the clones realised what they just did (much later, the clones would realise the existence of the chip, and future encounters between them and surviving Jedi would find them trying to explain themselves to their once-trusted generals).
With the clones having served their purpose but still naturally loyal to the Jedi, Emperor Palpatine promptly retired the clone troopers and introduced the Imperial Stormtrooper Corps. Stormtroopers will be made up of birth-born human recruits who demonstrate unwavering loyalty. They pride themselves in being reputedly incapable of betraying the Emperor and his Empire. Stormtroopers, however, are inferior combatants compared to clone troopers, for they lack genetic modification, their training focus on militarised peacekeeping and suppressing insurrections rather than full scale warfare, and most of them have no battlefield experience.
As loyalists to the Empire, the stormtroopers will continue to pursue surviving Jedi throughout the Jedi Purge.
From the beginning, the clone troopers had been trained to be loyal to Palpatine and Palpatine alone. They were in league with him from the start. While they respected the Jedi as leaders, generals and warriors, they never forgot their true purpose of existence. Eventually, they realised that the Jedi could be fooled - and if they could be fooled, they could be killed. One legendary quote best describes the state of a clone's mind when Order 66 was issued:
"What I remember about the rise of the Empire is… is how quiet it was. During the waning hours of the Clone Wars, the 501st was discreetly transferred back to Coruscant. It was a silent trip; We all knew what was about to happen, what we were about to do. Did we have any doubts? Any private traitorous thoughts? Perhaps, but no one said a word. Not on the flight to Coruscant, not when Order 66 came down, and not when we marched into the Jedi Temple. Not a word."
Of course, Palpatine relied on blind obedience from the clones for the success of his plan, and that largely succeeded. In a few rare cases, however, individual clones' loyalty to their Jedi generals proved strong enough to overcome loyalties and genetic modification developed from birth, leading them to defy Order 66 and save their generals.
After the rise of the Empire, the loyal clone troopers would continue their service under the New Order, reformed into the Stormtrooper Corps.
"Armed with deadly new weapons, blazing new ships and shiny new armour, our presence let the galaxy know that the days of the Old Republic were well and truly over. We were establishing a new era, an era of Order and Peace."
There are various reasons why Stormtroopers are eventually inferior to clone troopers:
- Birth-born recruitment gradually increased during the Empire to supplement more expensive clones
- New stormtroopers, cloned or otherwise, are inferior to existing clone stormtroopers from the Clone Wars for the same reasons given in the Disney canon section
- At the end of the Clone Wars, Palpatine adopted Spaarti cloning techniques to complement Kaminoan methods, and would eventually prefer it during the Imperial period. While Spaarti clones are ready in a year compared to ten years for a Kaminoan clone, they have greatly reduced intelligence and combat effectiveness. It was a desirable trade-off: During the Republic, Palpatine needed Kaminoan clones of the best quality to destroy the Jedi. During the Empire, however, Palpatine's rule by fear and domination only needed expendable cannon fodder to overwhelm what enemies he has left by sheer numbers alone. Even during the Clone Wars, many Kaminoan casaulties in the later years had started to be replaced by Spaarti clone troopers as filler.
As clones, stormtroopers continue to execute their core purpose of purging the galaxy of Jedi.
Clone troopers are genetically superior war veterans trained for wartime, while stormtroopers are largely/wholly birth-born recruits trained for peacetime. Depending on which version we look at, the methods used to ensure compliance to Order 66 between clone and stormtrooper may be same or different, and stormtroopers may be replacements for retired clones or simply a rebranding exercise coupled with technological reform. Eventually, however, stormtrooper combat effectiveness deteriorates and become inferior to Clone War era clone trooper effectiveness for similar but not identical reasons.
Star Wars Episode II: Attack of the Clones
CC-7567 ("Captain Rex"), 501st Clone Battalion (Star Wars Rebels Season 2)
Journal of a trooper of the 501st Legion (Star Wars Battlefront 2)
Order 66: A Republic Commando Novel