There isn't really a meaningful difference; either way the immune system is responding to a protein and "remembering" it.
mRNA breaks down within a few days, by which point spike protein production by your cells has stopped, and the spike proteins themselves break down within a few weeks.
Inactivated virus would be broken down and excreted within a similar timeframe or faster; it's the immune system memory of the proteins that it encountered that persists.
It’s not like T cell immunity has whole SARS2 virus to model against, like it does with other vaccines employing whole, inactivated virus.