In reality, a competitive enzyme immunosorbent assay and a sandwich ELISA really are apples and oranges. It’s dependent on your analyte that you’re measuring and several critical reagents to determine the sensitivity of the assay.
Sandwich-type assays are usually not good for small molecules simply due to steric issues; there needs to be space to permit two different antibodies to bind efficiently. So if you have a small enough target molecule, the competitive format may come out ahead of the sandwich for sensitivity.
Another thing to consider may be the units you are using for sensitivity. Since competitive assays are detecting small molecules of 5 KDa or less, their sensitivity may appear higher when measured in ng/mL. However, when converted to molar units, sensitivity is often similar.
With a competitive format, you might have more interference, as there is only the one ligand-binding interaction. The sandwich has two ligand-binding steps, which ensures that if one binding step is affected by an interfering molecule, it won’t affect the other. Some assay procedures deal with interference by dilution, which would affect sensitivity. On the other hand, more critical molecules = more complication, which makes it more likely the assay will have a weak link somewhere.
To sum up, there’s really no fixed rule on which of competition or sandwich ELISAs is more sensitive, since it depends on so many factors – reagent selection, steric issues, maximization of signal to noise, precision of pipetting and reagent handling, etc.