The standard engine in a Special (I have a 49 Special) is a 100 HP one barrel, and the Deluxe had slightly more 112 HP, with a 2 bbl carb. Basically, you should determine which is the better engine as far as running characteristics, oil consumption, compression, and go from there. Otherwise, they should both be the same internally, I do believe. The better engine to HAVE in your car would be the 2 bbl version, as that came with a Deluxe, so it would be more correct, but that being said, you could make the 1bbl into a 2 bbl. There may be some difference on the outside of the engine as to bolts, linkages might be slightly different etc but it should all interchange nicely. Someone chime in here if I am completely wrong on some detail...
Deluxes often came with overdrive, and if your Deluxe has it, so much the better. Do you have just the two engines, or two cars? If you have the two cars, ie a Special and a Deluxe (or if you can get your hands on the Special R/A), AND your Deluxe has overdrive, then you could consider putting the Special rear axle in place of the Deluxe rear axle. The Special (no overdrives normally available) had a 4.09/4.10 rear axle ratio, and the Deluxe with overdrive had a 4.55/ or 4.56 R/A radio. What you would get would be 1-2-3 like a Special in acceleration but with overdrive in 3rd it would almost be like a 4th gear, and so much better for more modern speeds, keeping the engine cool, and reducing noise. What the Deluxes had with the numerically higher R/A was much better takeoff, with something somewhat equivalent to a 0.8-1.8-2.8 and overdrive 3rd 3.2, if you get what I'm getting at.
Basically, overdrive overall got you better acceleration and slightly better top end speed, back in the day. By using the Special R/A with overdrive, you forgo the better acceleration and get much better top end at much lower revs.
As well, remember you have to change the speedo pinion gear as well to get the speedo to match up.