I have only a limited understanding of the details of BACON, but from what I remember it was what is called a "production system" and somewhat akin to an evolving expert system. Something like BACON starts out with a set of rules and then tweaks them looking for patterns that can be generalized into new rules. Novel for the early 80s, but in practice these systems seemed to be limited to very specific domains.
Eureqa is a genetic programming system (running over a graph encoding, bonus points for that one :) that evolves a set of rules from basic components to fit a set of data and hopefully be able to make future predictions. The general concept is not really new -- some of Koza's early examples of the power of GP were evolving Kepler's third law using astronomical data points as the input and evolving Ohm's law in a similar fashion[1] -- but developing a general toolkit and packaging it as a useful tool is somewhat novel. One thing that probably distinguishes Eureqa is that I would expect the output to be more parsimonious than that developed by a production system like BACON. A system like BACON is also more complex, involving various layers of detectors and rule emitters, while a GP system can be very simple once you have figured out the best set of operators for a problem domain.
[1] It should be noted that BACON did these tasks as well, so they are more of a general rule-building yardstick and put GP at a similar level to the well-developed (and well-funded) production systems research of the era.
