My thought would be that the T206 picture is correct. Paul Davidson was with Indianapolis in 1908 and 1909. Bill Davidson had only 7 at bats in 1909 when the T206 was created, so doubtful the T206 designers had a photo of Bill available.
You can't always count on the MLB Reference photos to be correct, as evidenced by the Krueger/Kruger example on my website, but their Bill Davidson photo is clearly someone other than the image used on the cards you showed us.
__________________
$co++ Forre$+
|