Yes the theory about the higher hydrogen content in nat gas will produce more water and hence the heat needed to evaporate it reduces the available heat is true in practice,if you compare "apples with apples".
However as Jonkatz points out excess air is generally left higher with fuel oils which could negate this advantage. Heavy oil burners are capable of running with lower excess air, but because they are more likely to go rich and produce soot, an extra margin is generally left or their combustion must be monitored more closely.
Other factors to consider (for and against):
1) The nat gas flame is far less radiant which means that less heat transfer takes place in the furnace so the gas exiting the furnace is hotter than in the oil fired version. The convection passes then must be able to compensate, but often more heat is lost up the stack. This fact needs special attention on firetube boilers where the higher temps entering the first tube pass can result in metal overheating and eventual cracks in tube and plate, especially if there is scale on the waterside. On old boilers a derate is prudent when converting to NG.
2) The radiance of the oil flame is actually glowing carbon, which must be completely burnt. But there is always a tendency to deposit soot on the heat transfer surfaces (tubes)which reduces the heat transferred to the water and here again will raise flue temps. Obviously regular soot blowing will keep this in check. But you're using steam for this.
3) The burner on nat gas will usually have far better turndown than on heavy oil. This may be of advantage,depending on your type of operation, as the burner will fire longer instead of cycling ON/OFF if the cutout pressure is exceeded. Fuel efficiency on NG will be better in this case.
4) Assuming you are using steam atomising for the heavy oil, this is not needed for nat gas. So a steam saving.
5) Nat gas is actually quite slow burning and if furnace conditions with regard to dimensions are not suited complete burning at furnace exit may not be complete and excessive incomplete emissions (CO) will be produced. This is also true with too much combustion air chilling the flame. Generally however the production of excess CO is an enviromental consideration as the efficiency gained in reducing it will probably not be practically noticeable.
Hope this helps. Rod Nissen.
Combustion & Engineering Diagnostics
nissenr@iprimus.com.au