Executive summary: Complex I and Complex II are separate routes in to the electron transport chain. Glucose favours Complex I, fat favours Complex II. Now the extended version:
Here we have a nice schematic of the electron transport chain in a diagram of a mitochondrion taken from Wiki images.
The ATP Synthase complex shown on the upper left of the mitochondrial diagram allows protons from outside the inner mitochondrial membrane to pass back in to the mitochondrial matrix, generating ATP in the process. Under White Non Smoker conditions this electro chemical gradient might well have been maintained for free by the geochemistry of serpentinisation plus an acidic ocean. Nowadays the combined pH and electrical gradient which drives this ATP factory is maintained by the electron transport chain. This transports positively charged protons out of the mitochondrial matrix to maintain the gradient which is dissipated during ATP production.
In the diagram you can see two versions of the ETC being driven off of the citric acid cycle. On the upper right hand side a molecule of NADH provides electrons to Complex I. Complex I pumps some protons, hands the electrons to the Coenzyme Q pool (CoQ, marked as Q on the diagram) of electron transporters which then hand them on to Complex III. Complex II is not involved. The CoQ pool is a mobile reservoir of redox shuttles (electron transporters) which hands electrons to Complex III.
The second version, shown on the lower area, has succinate feeding in to Complex II. Complex II is actually the succinate dehydrogenase enzyme of the citric acid cycle. It is built in to the wall of the inner mitochondrial membrane and hands its electrons to the CoQ pool directly, no Complex I involved. Another difference is that Complex II doesn't pump any protons.
The proton pumping done by electrons passing through Complexes III and IV is independent of their route of entry to the ETC. Anything feeding in to the CoQ pool feeds onwards through Complexes III and IV. Mostly.
So we have the citric acid cycle processing acetyl-CoA to a ton of NADH for Complex I and a smidge of FADH2 within Complex II.
The FADH2 is quite tricky. It is embedded deeply within the succinate dehydrogenase enzyme and never, as far as I can make out, goes anywhere. It flicks between the FAD and FADH2 state as the citric acid cycle turns and basically acts as a bridge to transfer the effective oxidation of succinate to the reduction of the CoQ couple.
Another route in to the ETC, which seems sorely neglected, is Electron-Transferring-Flavoprotein Dehydrogenase, which sadly has no handy name. ETFD sits in the inner mitochondrial membrane and passes electrons to the CoQ couple, much as Complex II does, also without puming protons. ETFD gets its electrons from the FADH2 of an electron transfer flavoprotein which, thankfully, gets its electrons from the FADH2 of acyl-CoA dehydrogenase, the first enzyme of beta oxidation. Back on home territory.
So fatty acid beta oxidation feeds in to the ETC at a "Complex II-like" membrane enzyme. It uses FADH2 to do this. It generates a small amount of NADH as well.
So we have two non-Complex I inputs in to the CoQ couple.
Aside: There are three if we include glycerol-3-phosphate dehydrogenase. Four if we include glycerol-3-phosphate oxidase Probably more. But let's keep it simple and stop at two... Actually glycerol-3-phosphate oxidase is really interesting as it specifically generates H2O2 enzymically. H2O2 production is generally considered to be a Bad Thing. Now what might the deliberate generation of H2O2 be signalling? Very interesting! Maybe another day.
So the citric acid cycle inputs just a few electrons through FADH2 at Complex II compared to the number it supplies using NADH at Complex I. Glycolysis is even more Complex I focused as it only adds NADH to its acetyl-CoA generation. However beta oxidation markedly inputs through the FADH2 of ETFD, with relatively little input using the NADH from the beta oxidation process, again in addition to generating acetyl-CoA. Obviously all acetyl-CoA generates the same ratio of NADH to FADH2.
The actual biases can be seen from these numbers, nicely posted by Lucas Tafur here. A direct quote:
As you can see glucose produces 5 molecules of NADH for each FADH2 where as fat produces only 2 molecules of NADH for each FADH2.
Glucose drives complex I significantly harder than fat does. Fat drives with a "Complex II-like" bias, supplying FADH2 from ETFD much as succinate dehydrogenase supplies some FADH2 from acetyl-CoA.
Both FADH2 inputs do exactly the same thing to the CoQ couple, they reduce it. A reduced CoQ pool has major implications for electron transport and free radical generation.
I rather like eating fat. What does that do to Complex I?
It's probably not the obvious answer.