From a pure CPU processing standpoint, if you check out the Geekbench results you'll see there are a number of MBA and 13-inch MBPs that have better scores than your quad-core Mini.
Comparing clock speed across different CPU generations is meaningless, a newer, "slower" CPU with fewer cores can easily out muscle an older, "faster" CPU with more cores.
Your Mini is about 1/8 of the way down the page.
http://browser.primatelabs.com/mac-benchmarks
That link doesn't show any 13" notebooks with a higher score than the 2011 Mac Mini server.
For Logic, the quad-core (even the "slow" one) will still be able to handle more tracks and more simultaneous plugins, but honestly you'd have to try really really hard to reach the limit of either CPU.
I have Logic X and run it on my 2011 server, as well as my 13" rMBP with a 2.5GHz dual core i5.
My anecdotal observations:
I have actually used both right next to each other to compare performance.
Logic starts up more quickly on the notebook, even though both systems have an SSD. My Mini has an aftermarket Crucial M4. However, my Mini also has a lot more plugins that it has to load, while my notebook has very few (only have the 128GB SSD).
Likewise, the demo song also loads more slowly on the Mini.
Much slower, in fact. Twice as long. I can't figure that out since it's loading from an SSD in both cases. Maybe the Samsung SSD in my Macbook Pro handles loading all those small files better.
Once everything is loaded, the Mini is quicker to switch between view sets, open plugin windows, etc.
While playing the demo song, the CPU tends to hang around 90% utilization on each system. However, the quad-core has more "headroom" since it will max out at 800% whereas the dual core maxes out at 400% (2 cores x 2 threads).
That said, Logic does run fantastically well on my mere 2.5GHz dual core notebook; really the CPU shouldn't be a factor unless you are going to run dozens of audio tracks simultaneously.