I agree that the answer depends on so many factors. I generally collect only Type 1s, but there are a few Type II and Type III photos I have that I still really enjoy. To me a good type II doesn't feel too modern, it must retain the warmth and clarity of a Type I. This circa 1930 Type II of Cobb at the 1907 World Series fits that bill for me.
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On the other hand, look at this 1911 stamped photo of Baker taken by Conlon. I love the 1911 stamp just after the famous World Series where he belted his namesake home runs and the image is relatively good for a Type III, but it is still missing the warmth of the Cobb Type II above.
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As I have not seen Type Is of the above images I am thrilled to have each, but still they they are worth a small fraction of what Type Is would bring. Type II and Type IIIs each have winning attributes, but it is tough to beat the combined warmth, clarity and moment in time aspect of a true Type I gem.