In Bohm's book Wholeness and the Implicate Order (which you can download for free here http://www.gci.org.uk/Documents/DavidBohm-WholenessAndTheImplicateOrder.pdf ) in chapter 8 "Steps Toward a More Detailed Theory of Hidden Variables" he puts forward a program for developing a theory of global hidden variables. His program aims at finding a sub-quantum level of knowledge that would account for the measurements we make, all of which are at the classical level.
I think the big difference between the two interpretations is that CI asserts that it is not possible in principle to find such a deeper level of knowledge. Bohm considers the possibility that there may be a way to account for the indeterminacy of QM by way of a theory of global hidden variables that would yield a verifiable understanding of an underlying relationship between measurements.
In as much as theory determines the kinds of experiments performed, which measurements we make depends on our theory. So, if the same measurements are made we would get the same results. However, given the different theories, we would not be making the same measurements.
As a case in point of theory leading to measurements particular to Bohm see this quote from the Wikipedia page for D. Bohm https://en.wikipedia.org/wiki/David_Bohm
In 1959, Bohm and Aharonov discovered the Aharonov–Bohm effect, showing how a magnetic field could affect a region of space in which the field had been shielded, but its vector potential did not vanish there. That showed for the first time that the magnetic vector potential, hitherto a mathematical convenience, could have real physical (quantum) effects.
There is on that page a schematic of an experiment that later confirmed his theory.
A very good explanation of the significance of theory to measurement (regarding entropy, but widely applicable) is given by E.T. Jaynes in The Gibbs Paradox http://www.damtp.cam.ac.uk/user/tong/statphys/jaynes.pdf section 9, bottom of page 13:
"...the theoretical explanation would predict generalizations; the range of possible nonequilibrium conditions is many orders of magnitude greater than that of equilibrium conditions, so if new reproducible connections exist they would be almost impossible to find without the guidance of a theory that tells the experimenter where to look."