Before telling if you should use a transformer or a converter, let me tell you that your device may work without any converter. Recent gadgets which are typically carried across the globe by the travellers are compatible with full range of voltage from 100v to 240v. They include mobiles, cameras, laptops, electric razors etc. But check the input voltage rating nonetheless. It should be printed something like "Input: 100-240v". The output voltage rating does not matter.
Now coming to the main point...You should be careful in choosing a converter
If I can to go into a little bit of technical details here, a transformer-based converter converts the voltage by elongating the sine wave of the AC current but still preserving the sine wave formation. On the other hand a solid-state based converts just chops off the sine wave to reduce the voltage, and hence the output current do not follow a sine wave formation. This kind of current is not compatible with all types of devices. But the pure sine wave form of current is compatible with most of the devices.
To summarize: The general rule of thumb is most of the electronic equipment (gaming consoles, DVD players, speakers, mobiles, etc) needs a transformer based converter. Whereas, electrical appliances like motor-based appliances, irons etc can work with solid-state converters. Transformer-based converters can be used for long operating hours whereas solid-state based converts are for short-term use (typically 1-2hrs). When in doubt, it is safer to use transformer-based converters. Also make sure that the wattage(W) rating is compatible. It is safer if the wattage of converter is atleast 25% more than wattage requirement of your device.
Pointers: link1, link2, link3