I was just talking with a friend - who went from a 4 to an X - about battery life. He asked me why I just don't go and get a new battery for my 6. I told him I don't know if this is a fully understood phenomena yet. In my case, my battery is typically at 40-50% at the end of the day. But it is definitely sluggish. Like when I called my aforementioned friend, from the home screen I pressed the phone icon, and it was an easy 3-4 count before the phone screen came up. Switch to Firefox, same thing. So it's slow, and CPUDasherX says I am running slower, but I have lots of battery left. I don't mind spending the $80, but I would if it didn't fix it.
It sounds like you have a perfect situation for a battery replacement potentially speeding up your device due to throttling. Check with a battery management app to see what battery capacity you have (not directly linked to age/potential for throttling, but will tell you 80% if you battery is healthy or not - since a healthy battery is a new battery most of the time).
That's my line of thinking in this, anyway. Either that, or if you noticed a significant slowdown from going from one OS to the next (obviously that would not be a battery issue, if the change was immediate).