As far as I know there have been comparisons with often ambiguous results. Federalism seems to make sense in some contexts (usually when social heterogeneity is significant) and less in others. Take a look for example at the preamble of this article (from APO):
FEDERALISM does not get good press in Australia. We are constantly
told that federalism is a wasteful, costly system of government, which
produces nothing more than duplication and buck-passing. Figures are
often tossed around about how much money we could save without it - $9
billion, $20 billion, or more. Australians have been brought up to
regard federalism as an archaic, inefficient and uncompetitive
encumbrance that is holding us back economically and socially. Yet in
other parts of the world, federalism is seen as a modern flexible
system of government, which is efficient, highly competitive and best
suited to deal with the pressures of globalisation.
The article Are Federal Systems Better than Unitary Systems? (1) (Gerring, Tacker, and Moreno, 2007) is also a good source of information. After an extensive analysis the authors seem to conclude that there are advantages to the unitary system (I find it a bit "blind" regarding historical and societal subtleties but admittedly that was not the purpose). You'll find plenty of others publicly available online.
(1) The authors specifically ask for readers not to quote or cite (since its a draft). I've chosen to do so because the paper seems relevant. No harm intended.
I know its not your question but I would like to introduce here a notion that is likely very relevant. A Unitary State is not equivalent to centralization. An Unitary State can decentralize services if needed (see for example Sweden). As so many of the apparent advantages and disadvantages commonly attributed to any of those two systems can actually be solved with either more centralization (saving costs and making a process more efficient) or decentralization (accounting for different needs in different areas/regions). This is also often compared to Regionalisation (different from Regionalism) and Autonomism (like Spain).
Historically Federalism tends to decentralize geographically. These separations are often made due to cultural identity (and perhaps more often than not Regional Identity, although different situations are known). This is perhaps the greatest caveat for this type of decentralization since many problems don't necessarily correlate with this. Good regions for education and healthcare governance, for example, don't have to overlap with good regions for security or water management. This delicate balance between centralization and decentralization is difficult and we still lack a lot of good case studies for different models of it.
One last point that I would like to mention is the flexibility of the current Federal systems. It's not an accident that Frankfurt has beaten cities such as Paris for the race to start to build a new London in EU. The state of Hesse (in Germany) has offered numerous advantages difficult for a unitary state (such as the one where Paris is). You'll see other example of regions that did good, at some point, under this system (Texas). On the other hand, failing to provide similar quality of life among different regions in the same nation (as it will likely happen in a strongly competitive system) can lead to polarization with all the consequences that implies (and some of them we are even witnessing today).