When James gets angry he explodes. He is like thunder and lightning and the wrath of God wrapped up in a human package. You can't reason with him, you can't stop him and you can't change his course. He is a storm in human skin that can barely be contained. The best thing you can do is hide until the storm passes. And it does.
They always say to crouch down on the balls of your feet if you see lightning. And maybe that helps you survive in the moment, if you are lucky, but after, after the lightning goes through you, the fire of the Gods flaming through your veins you always flinch at light. This is not something you can forget.
But while his temper is like a bomb going off his anger doesn't last long. He doesn't hold a grudge. He is just like lightning, he comes, he burns and then he fades away. He always laughs after he comes down from his anger, to let others know he is safe again.
(he did hold a grudge, for a brief moment when staring down Voldemort's wand, screaming at Lily to run. It was brief yes, but it was also the longest grudge he ever held).
When Sirius gets angry, properly angry, he gets quiet, cold, expression dead. He is like the heart of the winter when the wind rips everything in its path and the cold creeps into the marrow of your bones and it is so cold that you can't feel anything and your breath is like a cloud. He's so cold that you don't think you would ever be warm again.
Being around him then, you know all hope is lost. You start by losing all feeling in your hands and feet and bit by bit the cold creeps in and soon you can feel your heart freeze over and your lungs choke on air. Every thought and every movement freezes and you are left fading away, the only thing left behind being the ice on your eyelashes.
People expected him to inherit his mother's shrieking fury but instead he got his grandfather's coldness (out of all of them he is the most like Arcturus, oh he tries to deny it of course, hating and rejecting any association with his family).
You don't expect it (because you don't want to see) but you can see traces of the winter in him even when he's not angry. There's a ruthlessness in him that only the cold has. Winter is merciless after all.
When Remus gets angry it's different. He doesn't shout, he doesn't express himself in a different way but if you watch carefully you can see the tension in his body rising slowly, muscles coiled and prepared and there's something quite feral about his eyes.
He smiles and you feel the hairs on your neck stand up, everything in you telling you to run but you know it won't do a bit of difference because you can never run fast enough to escape.
He is like the predator patiently following you in the forest until you can't run anymore and you stop because you have accepted that you can't escape him.
He is the hurricane coming and you can only stand and watch everything you love get ripped apart. You are powerless before the wind.
When Peter gets angry, he turns red and he clenches his fists, trembling with the effort to keep himself still. He is like the earthquake you don't quite see coming but fully expect. And when he calms down, he folds onto himself like he could hide away. He regrets getting angry and the guilt builds up and he runs because he doesn't want to deal with the consequences.
Bonus:
When Lily gets angry, she is like fire. She burns everything in her path with absolutely no care for what she destroys around her. Only when the fire stops raging does she look around her but she isn't sorry. Fire is never sorry. Fire is a force of nature, she burns everything around her so something new can grow.
(Voldemort learns this the hard way, body melting, skin crackling and melting off, his pained screams being swallowed by the crackling flames. He burns and from his death, hope is born
seventeen years later, he burns again, Harry's anger enveloping him and flames rising around him again, he forgot the power of true anger).