The key factor in determining how much torque is available for a synchronous motor at startup is this: Is the intention to operate as an asynchronous start - or to supply power to the synch rotor field at zero speed and effectively have a synchronized start?
If the operation is for an asynchronous start, then the cage material can be adjusted to raise the available starting torque significantly (compared to a "plain" copper bar). To do this, higher-resistivity materials are chosen. The progression is from pure copper, to brass, to bronze, to copper-nickel, to Monel, to stainless steel. As the starting torque goes up, the pull-in torque typically goes down - in effect, the designer is "weighting" the speed torque curve in favor of starting vs synchronizing.
When this is done correctly, a comparable torque profile can be achieved relative to a similarly-rated squirrel cage induction design. There will still be a slight discrepancy: after all, the induction motor has the entire rotor circumference to squeeze a winding into, whereas the salient pole synchronous motor only has about 65-75 percent of the "cylinder" due to the interpolar space.
Another advantage of this approach is that it tends to drive DOWN the required starting current (same volts applied to a higher resistance circuit means lower amperes). Then again - synchronous motors are generally a lower draw than a similar induction design. As a rough estimate - the synch machine typically is designed to draw roughly 70 percent of the induction motor.
Better yet, excitation current can be delivered to the synch rotor winding from a standstill (either through an AC-AC rotating exciter, or by brush-and-collector from a DC source). This means the cage winding is along for the ride, and the real developed torque is that provided by the magnetic field strength resulting from the energized rotor winding. At very slow speeds (which is essentially what the "start" condition is), this current can be "forced" to a higher-than-continuous rating - which in turn means an elevated torque production. Admittedly, having to control two separately-powered fields simultaneously (the stator winding and the rotor winding) means more work for the variable frequency drive (VFD) programmers, but it does deliver significant torque advantages… AND reduces the inrush (starting) current to whatever the VFD wants to use as a "forcing" current for the stator winding.
The only real down side to a salient pole synchronous design is that it will probably be one frame size larger (in diameter) to accommodate the rotor design - but a correspondingly shorter core length, particularly for high-pole-count designs. The same cannot be said for the cylindrical rotor style of synchronous motor: it looks / tastes / smells / feels just like a wound rotor induction motor.