Main differences are:
ACA was developed back in the 1980s. ACBC in 2007.
Ratings vs. Choice:
ACA is a ratings-based conjoint--meaning that respondents rate how much they like the product on the left versus the product on the right, typically using a 7- or 9-point scale running from left to right. ACBC is a choice-based methodology where people choose which product they like best on a screen (choice-based methodologies are widely preferred nowadays compared to ratings-based approaches).
Partial-Profile vs. Full Profile:
ACA typically shows products on just 2 to 4 attributes at a time. So, if you are studying 8 total attributes, each product concept will be defined by showing levels from just 2 to 4 of the total 8 attributes. In the default ACBC approach, levels from all 8 attributes (assuming an 8-attribute study) are shown to define each product profile. Generally, full-profile is considered more realistic. However, ACBC can also be done as a partial-profile display if you take some extra steps. For example, you might be studying 15 total attributes, but decide only to take the most important 8 attributes for each respondent forward through the ACBC questionnaire.
Frequency of Use by Our Customers:
ACA is rarely used today (about 2% of all conjoint studies conducted by our customers). ACBC was recently used by our customers in 13% of their conjoint studies.
When to Use:
ACA should probably not be used if Price is one of the attributes. It understates the importance of price and cannot estimate interactions between price and other attributes. ACA could be used effectively for situations not involving price, where there are many attributes, such as 10 or more. A critical aspect to making ACA work well for you is to do a good job asking the "Importances" section at the beginning of the ACA survey. The documentation gives some advice regarding best practices (and one approach, if you have big enough sample size to make up for the loss of information at the individual level, is to drop the Importances question entirely from the survey). If you ask the Importances poorly, you will get poor results. ACA has a neat feature, which is the ability to compute utilities on-the-fly for each respondent as he/she takes the survey. ACBC cannot do that.
In general, most people prefer using the ACBC approach rather than the ACA approach. But, if price is not involved and if the Importance questions are asked well, ACA can do a creditable job. An example for appropriate use might be aspects of jobs leading to employee satisfaction.