Here is the math on how the research project work: they take your manufacturing output, divide it by 4, then run it through all your research or economic bonuses. Here are some of the ramifications:
The break-even point is +300% manufacturing. Until then, you are better off using your slider. At exactly +300% manufacturing, setting the slider to 100% science is the same as 100% manufacturing with the research project. Above +300% manufacturing you are better off using projects than the slider.
Assuming you could get the same research bonuses by replacing your manufacturing buildings with research buildings, early and mid game a research planet will out preform a manufacturing planet doing a project, but the manufacturing planet has the ability to produce manufacturing, research, or credits depending on your needs. Late game however, a planet with partial manufacturing and partial research can out perform a pure research planet.
Here are some idealized numbers run through the actual formulas. Note: For this exercise I am assuming that you would get the same bonuses by replacing research buildings with manufacturing buildings and visa-versa. In the real game it will usually play out more in favor split-type planets due to one-per planet buildings and starbase modules.
Planet 1: 100 production, total possible bonuses +600%
+600% manufacturing using research project: 175 research
+300% manufacturing, +300% research using research project: 400 research
+600% research using slider at 100% research: 700 research
Planet 2: 100 production, total possible bonuses +1000%
+1000% manufacturing using research project: 275 research
+500% manufacturing, +500% research using research project: 900 research
+1000% research using slider at 100% research: 1100 research
Planet 3: 100 production, total possible bonuses +1400%
+1400% manufacturing using research project: 375 research
+700% manufacturing, +700% research using research project: 1600 research
+1400% research using slider at 100% research: 1500 research