If the data are different, what are the circumstances in which I should use one over the other?
The aggregate statistics from the ACS Summary File found through the American FactFinder and the data from the IPUMS ACS are both from the ACS microdata.
The ACS Summary File statistics are based on and weighted from the full sample of the ACS microdata.
The IPUMS ACS is a republished (and in my opinion more polished) version of the ACS PUMS that includes some extra information that can be deduced from other available sources such as technical documentation and geographic shapefiles. The ACS PUMS is also a reduced sample of the original ACS microdata. It is meant to be a ~1% sample of the population. If you want exact numbers, the ACS microdata has 5,454,957 people among 2,487,838 living quarters and the IPUMS ACS has 3,018,308 people among 1,501,119 living quarters.
Comparing the same estimate for the same geography (e.g. the uninsured rate in Kentucky) will yield slightly different numbers between the ACS Summary File and the IPUMS ACS.
If you are searching for statistics, try to rely on the estimates from American FactFinder. If you are searching for specific sub-populations not found in the ACS Summary File through American FactFinder, or are trying to get accurate standard errors for the differences between two estimates, then you might want to use the IPUMS ACS.
ipums acs and also the census bureau's acs data files have one record per person. they are microdata, so millions of individual respondents. american fact finder presents only aggregated statistics. it's the difference between an online table creator and actually having the original survey data set.
I will just pick up the margin of error question that gannawag asked in a comment.
Census Bureau uses successive difference replication variance estimation method to produce their standard errors within FactFinder. With PUMS, you need to run your analysis with replicate weights using statistical software that supports them (Stata, R, SAS, SUDAAN; this is pretty much it -- SPSS does not do replicate weights, and I have no clue about other packages).
As far as the FactFinder goes, my guess is that the Census Bureau mass-produces the margins of error for the Summary Files, and then aggregates them for other levels of geography, rather than running them from scratch when producing the tables on the fly (the response time is just too fast). Or may be they mass-produce those margins of error for all levels of geography they support, but only release some of them in the Summary Files.
As @Kotebiya explained, the estimates should be expected to differ between FactFinder and PUMS analysis. The same comments applies to the margins of error, as well.