Mikael is right - paddles are easier to learn on: the tension is built-in and there is no cupping/curling of leather to overcome.
This does not mean that you will never damage a paddle - you will get the same nicks as any strop if you flip the blade over at the wrong time.
The primary benefit to me though, is that if you are going to use abrasive pastes/powders/sprays then a paddle is best because of the rigidity - every time you strop a bevel on a hanging leather strop (more so on a linen/leather combo hanging strop, as linen is slightly more abrasive than leather) you round the bevel a little, because there is always an amount of slack in the strop. With older blade types like wedges this was not a problem - and even desirable - as it saved you from honing the razor and a lot of the old wedges were sharpened almost exclusively on strops, as the (intentional) slack worked a plane at the apex of the wedge, saving a lot of metal removal.
With hollow grinds the effect over time of rounding the bevel is detrimental and leads - sooner or later - to the razor going back to hones for a bevel re-set. If you use abrasive pastes, etc, on hanging strops thane this becomes sooner rather than later in most cases, as it is very easy to take off a lot more metal than intended.
Travelling is a good point - paddles are obviously smaller (in most cases) than hanging strops and more durable, but certain leathers lend themselves admirably to hanging travel because they can be rolled-up. This includes kangaroo, cordovan, thin latigo and waxed/oiled juchten to name a few. The one thing these leathers have in common is that they are very thin compared to normal strop leathers (around 2mm thick or slightly less, compared to 4.5mm thick or thereabouts) and their surface treatment which does not encourage wrinkling. The first two - kangaroo and cordovan - excel in this respect, but both are hideously expensive as a raw material, even more so by the time a strop has been made out of them.
Regards,
Neil
