What is the Planck scale magnetic field strength?

Using the constants $mu_0$ (or $varepsilon_0$), $c$, $hbar$, $e$ and $G$, it is possible to define two quantities with units of magnetic field :
begin{align}
B_1 &= sqrt{frac{mu_0 c^7}{hbar G^2}} equiv sqrt{frac{c^5}{varepsilon_0 hbar G^2}} approx 8 times 10^{53} , mathrm{T}, tag{1} [12pt]
B_2 &= frac{c^3}{G e} approx 3 times 10^{54} , mathrm{T}. tag{2}
end{align}
Which one is really the Planck magnetic field?

While $B_2$ is simpler, I suspect it should be $B_1$, because it doesn’t use the electric charge unit. $e$ is not exactly as universal as $mu_0$. $B_1$ uses the Planck constant, so it’s consistent to call it a Planck “unit”, while $B_2$ doesn’t use that constant. Also, because of the square root, $B_1$ is a bit more of the same shape as the Planck length :
begin{equation}tag{3}
L_{P} equiv sqrt{frac{hbar G}{c^3}}.
end{equation}
The Planck units are presented on wikipedia: https://en.wikipedia.org/wiki/Planck_units but it doesn’t tell anything about the magnetic field.

We could also argue that $B_1$ is the answer because we can find it by equating the magnetic field energy density with the Planck density (dropping all the dimensionless constants) :
begin{equation}
frac{B_1^2}{2 mu_0} = frac{M_P c^2}{L_P^3}.
end{equation}
But then, we could also find $B_2$ by equating the Planck cyclotron angular frequency with the Planck energy :
begin{equation}
hbar omega_{text{cyclotron}} equiv hbar , frac{e B_2}{2 M_P} = M_P c^2.
end{equation}
Both methods are arbitrary.

So what is the Planck magnetic strength?