This is a very general statement which is not generally true.

The problem is related to the stability of the oxidation products:

borides form boron oxide/borates

carbides form oxides

The stability of the oxidized layer on top depends on the viscosity, stability, porosity and volatility of the oxidation product and on the application conditions e.g. temperature, oxygen content and velocity of the corroding gas.

Mostly I can agree with Dr. F. Kern. Please, read my papers on "ridge effect" phenomenon to understand the fact that the definition "oxidation stability" for transition metal carbides in general is absolutely uncertain.

To get a "big picture" view, I would start with an Ellingham diagram with curves normalized to the number of anions in the formation reaction.  It is a thermodynamic predictor of the temperatue of formation of  boron oxide, CO or CO2, the oxide of the counter ion, and the dissociation temperature of all these species.  Check the JANAF tables, or use a software program.    

The below link is  a concise interactive resource on the matter, for oxides and non-oxides

compounds.tp://www.doitpoms.ac.uk/tlplib/ellingham_diagrams/index.php                                 

You can also calculate the curves if you know the standard state enthalpy of formation, standard state entropy, and constant pressure heat capacity of the compound and it's (multiple) oxides of every atom you are dealing with. .  

But as Dr. Kern pointed out, the formation and efficacy of an oxide layer depends on number of chemical, physical, morphological, and kinetic properties in real systems.

Just to note... boron oxide melts at about 400 deg C to a highly viscous liquid that can flow to cracks into the any open porosity preventing further oxidation of the bulk material.  Above 1500 Deg C however, the boron oxide will sublime.  

Boron oxide alone may also form a glass or a ternary compound with the oxide of the counter ion, whose properties effect oxidation resistance.