In fact the difference is so pronounced that is is often hardly worth increasing the science percentage as you have to drop the spend so much that the overall science hardly increases at all while the production is significantly cut.
End of quote
I guess that it depends of the amount of free research you get for all of your paid research.
The F4 screen (with the spending rate), show you the paid military prod/ social prod/ research. The modification of the various sliders will affect what it is paid.
In the following example, you divert 100 BC for military prod to research prod , meaning that 100 BC are substracted to the paid militray production and added to the paid research. This can mean that overall spending rate and individual slider are adjusted, but at the end, the paid research has increase from 100 BC while the paid militray prod has decrease from 100 BC.
Now if the average for free research at empire level is that 2 BC in paid research give 1 BC of free research, you will have 50 BC of free research added to your research. So diverting 100 BC from military means increasing the overall research (paid + free) from 150 BC.
But if the average is 1 paid BC give 2 fre research BC, you will gain 200 BC of free research for just diverting 100Bc from military production. So diverting 100 BC from military means increasing the overall research (paid + free) from 300 BC.