Looking at the saves, there was 90 commerce and 99 corruption difference between the two games, which translates into 232 beakers per turn at 100%. If I subtract the income from Rome, I can still run 90% research rate, and still break about even with the 4th turn at as low as possible.
The main differences I see that would account for the base commerce discrepancy are that I built Commercial Docks just about everywhere I could, built a couple more cities in the FP area (basically amounts to using more coasts in low corruption areas), and that Rome had researched Communism so I could build Police stations.
Comparison of the two games:
Commerce: 4112 4022
Corruption: 1908 2009
Maintainence: 360 402
Unit Cost: 32 28
100% Res: 2228 1996
The Police Stations would account for most of the 99 corruption difference. The Commercial Docks, and extra coast tiles being used in the FP area, would account for most of the base commerce difference.
You did better than me as far as specialists, mainly due to using size 12 'corrupt' cities everywhere, instead of my many size 6 cities. The commercial bonuses meant you were getting 3 commerce from the size 12's, and I was only getting 1 from the size 6's, and the specialist to laborer ratio was higher in your game than mine. You were getting more commerce out of those corrupt areas, and I was getting more score. Some of that difference would have diminished if I had continued rushing Aquaducts/Marketplaces, but even then I think you had a better city placement in 'corrupt' areas from a commerce standpoint.
Smith's seems to have made more difference in the number of improvements I felt comfortable building. Since I wasn't paying for the Markets, Banks, and Stock Exchanges, I instead was able to afford to build Factories. So the difference in commerce wasn't huge, but the difference did show up in production quite a bit.
-------------------
Being attacked by Rome sounds like one of those random things that just happens from time to time. There couldn't have been much difference in our games by that point.