In addition to this, you have to consider where they sit on the map.
The Dardanelles looks more strategic from a Black Sea perspective and a completely modern naval point of view.
But this was Rome, while shipping and trading was important, this was not just to become a trading center, but a very important city. So defense as others have stated was the key. And foot soldiers were very important.
Crossing the Dardanelles is harder than crossing from Anatolia towards Byzantium, not so much because it was a harsher gap, but because of the overall logistics to take an army to the city of Dardanelles or Abydos. Also, the narrow passage from Gallipoli towards mainland Hellas was never a friendly zone, so I suppose they had to improve that area significantly if it was to become a main center for the Romans and it did not offer that much of a strategic advantage, had marshes and was rather flat. And on top of that, they would still had to fortify the Bosphoros crossing at some point.
The Dardanelles also did not have that much space for a large port and it was also twice as long as Bosphoros. You had to fortify a strait from Gallipoli (Hellenic mainland) towards the Dardanelles (modern city of Canakkale and further south).
I'd say that the Dardanelles are far more important today than they were in the past, but they did ensure that naval attacks to the city of Byzantium were limited, assuming you control the passage. But still, the Dardanelles had to be controlled on both sides, but it was rather wide, apart from the point of the actual city of Dardanelles, so I'm not so sure if it could have been a very good naval defensive point rather than some sort of an outpost. It's not like they could fire cannonballs, all they could do was send out ships to block passage. If you chased a navy out of the Dardanelles, you ended up in the Aegean sea. On the other hand, in Bosphorus (or north of the Dardanelles to Gallipoli), you end up in the sea of Marmara, with the strait of the Dardanelles acting as an outer wall. Feels better for naval protection imo.
Not sure if in the case of having different governments controlling the two straits today if one would be more valuable than the other, but they both are extremely important if you're going to or coming from the Black Sea.