acid base - Which is more acidic BF3 or AlCl3?

Which of the species $\ce{BF3}$ and $\ce{AlCl3}$ is more acidic, both are electron deficient.

In case of $\ce{BF3}$ one can argue that there is extensive p-π-p-π back bonding and as a result the electron deficiency is less.
That means that the positive charge on the overall molecule is less.

In case of $\ce{AlCl3}$ one can argue there is p-π-d-π back bonding and as a result the electron deficiency is more in case of aluminiuim.

Therefore the overall positive charge on the molecule is more, meaning it is more acidic.

So $\ce{AlCl3}$ is more acidic that $\ce{BF3}$ is conclusion of the above factors. Is this plausible?

I also faced the counter logic that $\ce{BF3}$ being a small compound tends to react more readily and therefore is a strong acid.