I ended up taking some post-bac courses at the university I'd gone to for my BA then going directly into an MS program.
1. Getting re-admitted to ones alma mater is simpler than a new school (given that these are adults going back to school who may well have moved and established families, their alma mater quite possibly is no longer an option)
2. How many credits were waived? This is a pretty serious sticking point, as anything > 2 year full time equivalent becomes a major time commitment & investment. I would also point out here that this can vary significantly by institution, unfortunately.
3. Many undergrad classes don't support a fully flex part time schedule (or, severely limit their evening & part time options). This becomes increasingly important in this scenario.
While there may or may not be an admission-department policy or stigma against second undergrad degrees, the system is by and large certainly not geared to encourage it as of present.
But the question here is what is best for the poster.
Assuming he can pass the MS degree, a future employer will give much more credit to an MS than a second BS in CS. Furthermore, as he describes it, the coursework already includes the equivalent of an undergrad in CS or more.
source = me. i'm currently admitted back to my alma mater for a second degree in CSC and will be returning in fall this year.
The real issue is that the BS degree covers (roughly) 2 years of general study and 2 years in a major. Anyone that has already done the general study part just wants to do the 2 years part in another field. I think it is a failure of the academic system (in the US) to not break down the degrees correctly and to call those 2 years in another field an MS--should be a 2nd BS.
I will note that in Europe, a lot of the general study that US universities do in the first 2 years of a BS are done in the last two years of high school, for example the French baccalaureat (bac).