Regarding the differences in moist lapse rates I do remember seeing simpler, but less accurate formulas for estimating the moist adiabats. Is that what you're talking about Jeff D.? I ask because I believe that Earl Barker's skew-t moist adiabats are slightly steeper than I see elsewhere and I think this may lead to slightly higher CAPE values as compared to other sounding sites. I wonder if he is using a moist lapse rate equation that is slightly different?
Also, there are a couple of different ways of selecting the parcel for the MUCAPE calculation as well. You can brute force it by walking up the sounding and performing the CAPE calculation for every parcel and then select the one with the maximum value. Or, what RAOB does is immediately select the parcel level with the highest wet bulb temperature and just use that. Obviously, that is significantly more computationally efficient, but I wonder if it is at the expense of missing a more unstable parcel in strange (and not very likely) scenarios. Maybe John Shewchuk can comment more about this if he sees this post.
Anyway, the main takeaway (for me anyway) is that CAPE calculations can be very nuanced so making comparisons of the values obtained between different programs or even different versions of the same program need to done with at least some understanding of the potential issues.