/dbt/ I got an issue with my bike

>takes a YTX20 battery
>the one it came with is dead
>install a lithium battery i pulled out of my other bike thats comparable to a YTX9 (the YTX9 is smaller than the YTX20)
>cranks up excellently
>sweet, order an acid YTX20
>struggles to start
>weird, return it, get a lithium version of the YTX20
>still struggles to start
>get it tested, everything is good with the new giant lithium battery
>reinstall smaller lithium battery
>it cranks up right away

Whats the reasoning behind this? Dying stator not returning enough charge to the big battery?