Anyone visiting Pergamon Museum in Berlin could fathom a traveler's awe as they enter Babylon at its peak. With all its glory, the city lived up to its name, the gate of God. At the time, the city's strategic location at the banks of Euphrates and the size made it an important target for the armies to control core of Middle East. The city has changed hands many times until its complete destruction.
900 km from ancient Babylon there is another city, al Bab, the gate. The two cities share more than a similar name, much like Babylon, al Bab is the gateway to change destiny of a large portion of the Middle East for years to come. No doubt that the city's name would be forgotten in coming decades, but for now it lives up to its name, the gate. And it may be the gate to control Aleppo's, Eastern Syria's and maybe Iraq's fate.
Al Bab, a prominently Sunni Muslim city, is under Islamic State (IS) control since 2014, but IS may have given up on it as the race of two forces: Kurdish-led Syrian Democratic Forces (SDF) and Sunni-Arab Free Syrian Army (FSA), continues. IS has to wage a costly battle against two forces in two fronts to hold the city. Seeing it, it already moved its headquarters to Khafsa. Thus much like Jarablus, resistance could be minimal for the invading force. That said giving demographic structure of the city any non-Arab and non-Sunni force would have difficult time keeping the order in it.
Both FSA’s and Turkey's (primary supporter of FSA), determination seem to be very strong to control the city and/or prevent SDF from occupying it. Turkey’s position is well communicated and understood by all parties. Looking at the motivations of the other stakeholders a FSA occupation of al Bab is more likely.
Government forces/Russia/Iran could prefer FSA occupation of the city as it is much weaker than IS. A Kurdish occupation would not be preferred as it would link two Kurdish controlled areas and would put them in a strong position in future negotiations. Turkey-controlled rebels could be much weaker in negotiation table than the USA controlled Kurdish forces.
Islamic State would prefer FSA too. With Government forces and FSA engaged in battle, they would have more room to maneuver. Their main war would be waged against SDF and most FSA factions are ideologically very close to IS. Location of the new HQ is not randomly picked.
USA and the West would be happy to see IS cleared from the city; they seem to be indifferent at best between SDF and FSA. But occupation by FSA would not antagonize Turkey, a NATO ally with power to steer future of Syria. Moreover it would put to an end to the tension escalation between FSA and SDF and re-focus SDF's attention to IS, the primary goal of the USA and the West. As a side benefit it would also lower risk of an ethnic cleansing in the city.
Saudi Arabia and other MENA countries would also prefer FSA victory; after all they actively supported FSA. Also Kurdish forces are seen as proxy of the USA and the West.
What’s next? Baring another conflict with Russia, Turkey seems to be both willing and capable to prevent SDF advancement. FSA said to be spreading itself too thinly, but Turkey would be happy to keep status-quo once it occupies a comfortable area between SDF forces. Once the FSA re-establishes itself as an attraction point to other Sunni-Muslims and reinforces its ranks, it could act more aggressively against Kurds and government forces; Mambij could be a priority at that point.
FSA control of al-Bab would put a stop to Kurdish unification and would most likely create a temporary status-quo in northern border of Syria. Kurds, pushed by USA and their Iraqi counterparts, could move to south to weaken IS, which would make the war in Iraq against IS easier. I believe a Raqqa offensive is not in cards as it will not serve the best interest of Kurdish groups. Focus could switch to Mosul.