Two ways to look at it then, and you can decide which one is for you:
If you store in tempdb, the db will stay small and not get bloated because tempdb is dumped every time. However, in a reboot, you will lose state.
If you store in ASPState, you won't have to worry about losing state. I'm not for sure, but I imagine there is some type of process that purges expired sessions from the table, so this table probably won't become bloated as well.
Out of the two options, I would imagine that ASPState is the more popular choice. It is easier to setup and requires less security privileges.