Which has caused more deaths? Catastrophic Anthropogenic Global Warming or illegal immigration?

Considering that CAG is in question as to whether it exists but illegal immigration is not, I'd say the latter.

Global warming is a contributing cause to illegal immigration.

Of the two, I think vodka has killed more people. What? My answer makes no sense? Neither doe framing your your question about science and fact as a political question. so, I still say that of the two choices, it's vodka.

Almost certainly global warming. While it never says "global warming" (or "illegal immigration") on a death certificate, global warming has no doubt been a contributory factor in deaths from heat, flooding, tropical cyclones, etc. As an example, in 2008 Cyclone Nargis killed almost 140,000 people.

Most of the deaths from illegal immigration come about specifically BECAUSE IT IS ILLEGAL and the migrants are forced on dangerous journeys through regions of extreme heat and cold and have to deal with unsavory characters, such as "coyotes". Perhaps Sagebrush would like to legalize it to cut down on such deaths?

I would say the former.

I would expect death counts in heat waves to be an exponential function with temperature. A fraction of a degree difference could mean hundreds of additional deaths.