The main difference between slip ring and cage types is that the slip ring rotor generally has a much lower slip at full speed than the cage rotor if it is properly shorted directly at the rings. We need to check that the variable frequency drive (VFD) slip setting can go low enough. Otherwise only general things need to be considered......mainly the insulation quality of the stator since its likely you are dealing with an older motor.
The slip-ring motor has slightly different impedance response to a squirrel cage machine so the VFD control has to allow for this, but I believe most large VFD suppliers have this as standard. The slip-rings need to be short-circuited so the brushes can be removed (allowing maintenance-free operation) but this is never really a difficult procedure. There can be transient voltage issues on some VFDs (high power) but the OEM's usually have solutions for this.
The usual issues related to shaft voltages and earth brushes / insulated bearings etc. need to be considered. I would be surprised if any of the major variable frequency drives OEM's can't offer you a tried and tested solution - with minor modifications to the slip-ring motor. Of course there is also slip energy recovery which is used all the time for variable speed on slip-ring motors.
There are two types of torque that need to be examined. One is the steady state torque output - the kind when the machine is spinning merrily along at a constant speed. As long as the VFD can supply the voltage and current required to produce the torque, there's no difference between a VFD and a "line" source.
The second case is the transient (starting) torque performance. For a "standard" slip ring design, the torque is typically modified in some fashion by a control (liquid rheostat or equivalent) that effectively limits the starting current to some preset value. In the same fashion, it more-or-less controls the incoming line voltage. When operating on a VFD, the VFD "brains" do the controlling in a similar fashion. If the VFD programmer understands the application correctly, there's no visible difference in performance.