If it was a competition between english literature and greek philosophy you can be absolutely certain that the fixed amount would be a tiny fraction of what it is now.
Curing cancer, infinite amounts of cheap energy, staying competitive, winning against China both economically and militarily, you really think the size of the pie would be the same without these things?
Because the costs of not adapting to climate-related environmental change will be astronomical. I mean, would you say climate adaptation is on par with the importance and urgency of curing cancer? The arguments would be interesting.
Ultimately there is a fixed amount of effort people can expend - however the science budget isn't fixed in the sense that projects like the LHC can generate the excitement etc to enlarge the overall pie ( for science - taking away from something else of course - though that could be time spent at home unemployed ).
Most science is done through small incremental advances that add up over time - one of the problems with that is it's rather hard for politicians to see or understand that.
Big projects capture the attention. Though obviously big projects can also, if they fail, damage the reputation of experimental science as a whole.
So yes - LHC isn't probably the best use of money - there are more pressing immediate concerns - however on the other hand - everyone has heard of it - it attracts funding and people to science ( and does good science of course ).
Tricky balance.
This is a huge problem when the immediate extinction threat problems are global.
See the ssc as an example. Note also the nih is a massive fund (25+ billion in grants per year, all bio). Nsf is a better example because they have to fund many fields. Doe has fixed funding for nuclear, plus soft funds for scientists in many fields (they funded the human genome long before nih).