Thank you for the vote of confidence, Jim, but I am far from the most knowledgable about these two sets. Others like Scott B. and Brian McQueen know far more than I could hope to know about them. Nonetheless, I am quite familiar with both sets and feel that I can address their scarcity differences. In my opinion, E107s are far tougher than E103s. Since there are over 150 different examples of E107s (146 players plus a few team variations), it makes finding a type card of E107s not terribly difficult. The E103 set is much smaller, so finding a "type" may appear to be more difficult. Looking for specific players of one or the other can be tricky, however. Certainly, both sets have their commonly found cards and toughies, but if you take a middle of the road difficulty from each set, I'd surmise that E107 far outranks E103 in difficulty. I'd venture a guess that it is probably 3x harder to find a particular E107 than a comprarably difficult E103. Both E107 and E103 cards are tough to find in nice condition due to how thin the cards are. So, with both sets (but much more so with E107s), you sometimes have to take what you can get if you are looking for one of the more scarce cards in the set.
During the early 1900s, the caramel companies were competing with each other quite a bit and getting cannibalized. I think that the Williams from E103's Williams Caramel is the same Williams from Breisch-Williams (E107), but there was more than one Williams in the caramel game back then, so I don't have concrete proof of that. Brian McQueen wrote a very nice article in Old Cardboard a while back on the history of Breisch Williams. He may be able to confirm that link definitively based on the research that he did. Great topic about two of my favorite sets!
Just for fun, here is an example of each...
