Si & DX engines have the exact same crankshaft, Honda P/N 13310-PE2-020 and exact same connecting rods, Honda P/N 13210-PE1-000.
The engine blocks are identical except the Si block has the bolt-on oil cooler adapter, and the oil pan was different. Since oil coolers and oil pans are free, I would suspect this would be legal, but somebody might split hairs over this. The bore/stroke/weight/ of everything else is identical. Flywheels might be different but the DX unit should be a direct bolt-on swap.
The main difference, as others have noted are the pistons and head design. The Si had pistons with a very pronounced dish and the lowest CR. The DX had a modest dish and a higher CR. The HF had a different dish/dome config to give the highest CR of all three. HF conn rods are also very different than the DX/Si rods in that they are much lighter but are too weak for racing, and are not legal. HF pistons had one less oil control ring as well to reduce internal friction. Keep in mind, the HF was designed for economy, not HP!
The heads are completely different.
The Si had the best head for making power with a true 12V head. The DX had 12V plus the CVCC prechamber auxiliary valve. Some HF's had 8V plus prechamber. All three are very easy to spot by pulling the valve cover.
Note: Canadian DX heads don't have the CVCC prechamber and make a lot more power than US heads but are definitely not legal! A quick way to spot a cheater head is to note the angle of the spark plugs. The Si and CDN DX heads are similar in that the plugs install at a near 45 degree angle, while the US Dx head the plugs install at a shallower angle since the plugs protrude into the prechamber and not in the actual combustion chamber.
[This message has been edited by Greg Gauper (edited April 11, 2005).]