If all you care about is clamping the turn-off voltage to a safe level than it doesn't really matter all that much as long as the parts are used within their ratings. Sometimes you care about the time it takes to dissipate the energy stored in the coil, and then you care more specifically about what that voltage is, because initially the current through the clamp is equal to the operating current of the coil, so allowing a higher clamped voltage means more power which means it takes less time to dissipate the coil energy, and a lower clamped voltage means the current continues flowing longer. This is sometimes referred to as 'decay mode', low voltage provides slow decay, and high voltage provides fast decay.
So for example, in a power conversion application where you care about efficiency, a Schottky or an active switch arrangement that provides minimal voltage is better, because you want to maintain that circulating current in the inductor to reduce the downslope of the ripple current and avoid giving up too much of that energy. Same with PWMing an inductive load, you're injecting energy during the on period, and a low clamping voltage allows you to have a longer off-period/lower duty cycle because more energy stays in the load.
On the other hand, sometimes you want to dump that energy as fast as possible. For example in a solenoid actuator (of any kind, including those in relays), the actuator releases when the magnetic field collapses past a certain level, and field is determined by the current through the inductor. So if you want a fast release, you need to reduce that current quickly, and might want to use a TVS, a bridge driver, or even a resistor in series with a diode (since you know the initial decay current is equal to the operating current, you can set the initial clamping voltage through ohm's law). Whether or not this electrical speedup is significant compared to the mechanical speed of the actuator depends on the application.
I've done solenoid drivers that need both modes: slow decay to enable efficient pwm for peak-and-hold driving (applying a high power pulse to initially actuate the solenoid, then dropping to a lower power via PWM to hold it in place), and fast decay to allow a faster release. A quasi-full bridge driver with a high side switch and diode to ground on one side and a low side switch and diode to positive supply or a dump resistor to ground on the other can do that and is easy to drive. Turning on one switch and PWMing the other gets you slow decay and turning off both switches allows the coil voltage to rise to full reverse supply voltage (or whatever you set via the resistor) for fast decay. You could also actively drive both sides of the coil for more control but that's more complicated. Some motor drivers have this functionality built-in as part of their current control scheme, since they have internal current sensing anyway it's a lot easier to put this functionality on-chip than to build it up externally. There's a cute little Allegro full bridge driver with programmable current limit in SOIC8 that has a neat automatic decay mode control feature that I've used but don't remember the part number.
EMI is also a consideration of course, but would be anyway and there are auxiliary strategies that can address that.
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