I don't recall seeing any footage of Dillon & I tend to steer clear of predicting cross-era fantasy fights, too many unknown variables for me. Based on fights contested in & around LHW (above 164lbs & below 180lbs), I rank Bivins #8 all time at LHW & Dillon #20, for whatever that's worth. Bivins only had 15 fights in the weight range, but the quality he packed into those 15 fights is extraordinary. He went 14-1, with the only loss to my LHW #1, Ezzard Charles. He beat, and wait for it......Charles, Lloyd Marshall, Joey Maxim, Gus Lesnevich, Anton Christoforidis, Teddy Yarosz, Billy Soose, Nate Bolden & Curtis Sheppard. Jack Dillon was around 85-21-12 in this weight range, though his post prime numbers spoil that record. He was 40-0-3 & 55-2-4 in fights within this range. According to my notes I consider he lost 8 x LHW fights in & around his prime years, 4 to Billy Miske, 2 to Harry Greb, and 1 each to Tom McMahon & George Chip. He won 1 against Miske (1-4 in total), as well beating Battling Levinksy (5-2-2), Jim Flynn (1-0-1), Bob Moha x 2, Gunboat Smith, Gus Christie x 2, Jack Twin Sullivan, Vic Hansen, Charley Weinhert & Al McCoy (2-0-1). As you can see, Dillon has the greater depth to his win resume, having contested far more fights in this weight range, but I think Bivins has the better quality in the top 5 opponents he beat around LHW, whilst Dillon's losses after that initial great run at the weight hurt him a bit. Dillon is my #18 at MW based on fights contested in & around that weight division and he also did notable damage at HW. Bivins has a fine HW resume for his size, too. 2 x fighters with very strong arguments for top 50 p4p all time, factoring in their entire careers at all weights.
I have been on this forum for many years now, and I don't think that I have seen this one before. At the risk of echoing the previous poster, Dillion is better suited to the weight stipulation, and Bivins is a more accurately know quantity. You get the idea that Dillon was rather special for eyewitness accounts, but we don't have any film, and even poor quality film woudl constrain things a bit.