Question i5-11400h versus i5-12500h ?

Hi All,

I need some help. I want to get a new gaming laptop on sale, both are the Acer Nitro 5 with exact same specs except for the CPU.
The i5-12500h is 130,- more (877 to 999).

I'm not sure what cpu is actually better pair with the RTX 3060...
The i5-11400h has 6 cores and 12 threads, the i5-12500h has 12 cores, but only 4 P-cores.
Is the i5-11400h actually a better choice here due to 6 P-cores? The i5-12500h only has 4 P-cores but do the e-cores actually make a difference for gaming ?
I play cpu-intensive games like Battlefield so I do need a decent cpu for the rtx 3060 and high FPS.

Thanks in advance!