In theory, there should not be any difference between the two, but in practice spin-offs usually have the edge. Past a certain size, bigger actually get worst due to complexity and loss of visibility creeping in, departmental infighting, etc. Very often, you also get bigger because the people in charge either want to build an empire, or are actually compensated for growth rather than more sensible performance metrics. Sometimes conglomerates actually hide value due to a hidden assets, or even potential spin-offs.
Spin-offs actually have some structural advantages for investors due to forced sellers, less analyst coverage, a more focused management team that no longer have to fight for capital of departmental support, etc. (there is another thread where the benefits of spin-offs have been very well explained).
However, just as you have Berkshire, Singleton's Teledyne and others, some conglomerates do function well, provided they have sensible management at the helm, just as some spin-offs are doomed from their get go due to debt loads, or poor business prospects.
I have worked with very large Canadian and American businesses, and more often than not, bigger is unfortunately synonym with dysfunctional (dysfunctional can still be very profitable, just a far cry from what the true business potential would/should be.) In the end, it really depends on the perspective: bigger is often not a bad thing for management, but as an investor, I'll usually look first at spin-off before conglomerates.