Phil,
I towed a 1,000kg Triton and 1,300kg Troll with a 100bhp VW diesel Touran. This is the same floorpan as the Tiguan, same torque but less bhp. It was very stable but a bit slow.
Next up came a 900kg Familia and then 1,200kg Triton with a 110bhp diesel Yeti. Again this is the same floorpan as the Tiguan, same torque but less bhp. It was also very stable but a bit slow.
Currently 150bhp 1.5 petrol Audi A3 pulling my 1,200kg Triton.Again same floorpan. As regards pulling power this is my best vehicle so far. The petrol engine, a later version of the Tiguan 1.4 petrol is flexible with the torque across a very wide rev band.
The Tiguan with the greater kerbweight would be a more solid/stable tow, just a bit slower. More bhp would be nice with the 150bhp being better, but I would have no reservations in towing with the 125bhp engine.
Your Mazda from memory is a conventionally aspirated engine, ie no turbo. It lacks the torque that the Tiguan will have so probably why it struggles.

Colin