Tubes have inherently greater output impedance than transistors. This is a great oversimplification, but in general, output impedance should be lower than the impedance of the device being driven. Due to high output impedance, many tube designs have problems driving low impedance loads unless some form of impedance correction is provided. A transformer is one way to drop the output impedance of a tube amp, which makes it easier to drive low impedance loads. The lower the impedance of a headphone, the likelier that a transformer mode might be useful. That's why 300 ohm Sennheisers are likely to do better without a transformer than 40 ohm W5000's. The lower impedance of the W5000 will draw more current from the amplifier, and may be too difficult for the amplifier to handle.
For me the default is always OTL, since the best a transformer can do is be transparent, and precious few transformers actually accomplish this. I do not personally like transformer colorations in the sound. However, if OTL has difficulty driving a headphone, it can manifest as noise, poor low end, and possibly distortion. In that case, a transformer may be the only way to drive the headphone properly with that amp. Note that several manufacturers have designed tube amps that can drive any impedance headphone without a transformer.