On a Hue bridge the smart controls are paired with the bridge. That allows for more customisation but the switches cannot control the lights if the bridge is turned off.
On a Trådfri gateway the smart controls are paired directly with the lights. So they will keep working if the bridge is off. However, you cannot customise anything about the smart control configuration.
Of course you can always control the lights using non-smart switches. On a Philips Hue bridge you can change the power-on behaviour of lights: How to set up Power-on behaviour for my lights?. Trådfri lights will always switch on to previous state which cannot be changed.