What are the benifits to CoC frostbolt/ice nova combo compared to self cast fb/ice nova?

I like my self cast but a friend says coc is better. any thoughts?

CoC is way more pricey, but fast af boy

CoC triggers less damage, but can also trigger spellslinger

when manual cast can use archmage-unleash-spellecho


for coc, its more ezz to trigger frostbolt
for manual cast, you may need trigger frostbolt, or use 2 active gems

so in a sense it's the evolution of self fast w/ 2 active gems?