There is a world somewhere between reality and fiction. Although ignored by many, it is very real and so are those living in it. This forum is about the natural world. Here, wild animals will be heard and respected. The forum offers a glimpse into an unknown world as well as a room with a view on the present and the future. Anyone able to speak on behalf of those living in the emerald forest and the deep blue sea is invited to join.
To expand on the density topic, I'll use an example. A 200 cm body length, sub 100 cm shoulder height Bengal tiger attains a mass of around 270 kg. A lion of 200 cm and bit taller than 100 cm at the shoulder seems to attain 240 kg at best. Therefore, Bengal tigers are significantly heavier for their frame. The rest of the tiger subspecies, bar the Amur form, also seems just as proportionately heavy, with the island varieties being actually even more proportionately heavier. The modern Amur form seems equally as proportionately heavy as lion per the STP data.
As Peter pointed out, cursoriality is a major factor in mass proportionality. Lions lives in an open, treeless environment where endurance and speed must account for the lack of surprise. To be fast, one needs both a large stride, thus a big frame, but also light. By being taller and having longer limbs, lions cover a greater distance per stride, bringing about speed while saving energy by not taking extra steps to cover a select distance. Decreasing the mass stress on the frame is also essential for energy conservation and ensuring attaining and keeping high speeds are less stressful on the skeletal structure, thus lions went down that route as well.
Tigers live in densily forested areas for the most part, where surprise is not hard to obtain, thus no need to run further or longer. Moreover, the trees above discourage vertical size. With those factors, tigers must go a different route in their morphology.