Very different principles.
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The Motor Lug trailer carries the motorcycle lengthways, making the combined towing vehicle plus the trailer’s combined length longer. The Hydra-Trail trailer carries the motorcycle sideways, reducing the combined length considerably. The two trailers also reverse very differently, with the longer trailer much more likely to swing; the Hydra-Trail, due to its very different design, does not swing.
As you can see in this video, unlike a conventional trailer, the Hydra-Trail trailer’s wheel ‘swing’ (like a shopping trolley) so that the trailer will always track the rear of the towing vehicle:
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It can also deal with some pretty steep slopes:
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From a quick look on the internet, both trailers are similar in price. My TowPro trailer (see below) was cheaper but only in as much as I bought it roughly 15 years ago, when it was about £800. A lot of money then and now.
Your Motor Lug is much more similar to my very good TowPro trailer, as used by the AA / RAC etc. This too I can break down and carry in my VW Polo. It will carry heavy motorcycles, right up to my 1600 GT or a fully loaded Goldwing, with all the trimmings, a weight greater than the Hydra-Trail can manage to carry. As far as I can see, the Motor Lug’s maximum weight carrying limit is 350 kg ie. not sufficient to carry my 1600. The Hydra-Trail can mange up to 250 kg. This is less than the Motor Lug but easily sufficient enough for my Himalayan.