I agree with both the last two posts. The problem with space warp transporting is the energy requirements required to warp space to that degree (it would be exponentially more energy dependent like warp drive). Gary 7's transport was likely this kind of transport but it was nonetheless intercepted by a standard transporter. Perhaps this suggests that both use the same dimension as a medium.
Trek is so inconsistent though. Some have speculated that dylithium is a wibbly wobbly amplifier that boosts anti-matter output. More sophisticated amplifiers would boost energy output so races such as the Kevlans could travel faster and all Federation ships would need is stronger structural integrity fields to withstand warp stress. Presumably transporting a humanoid by warping space would require a strong structural integrity field to prevent the transportee from being ripped apart as well.