I never looked at the examples, but I do know the "s" core may have problems reaching 120Mhz due to the multiply/data shifting functionality.
I've seen the SOPC builder select the wrong frequency before (seems to grab a clock value from the design, but why it would choose 138Mhz I'm not sure). A lot of the time it doesn't matter what the SOPC is built for unless there is a clock dependent core in the design (like a UART). However setting it properly is in your best interest since some pipelining optimizations are possible if you select the value properly.
With the 1S10, if the design is not very busy you can probably reach 125Mhz (I think my fmax was 127Mhz), but go with sometime a bit less like 120 to give some breathing room. Other then that, if you understand how to create a design like the ref. designs then I think you shouldn't see any problems (test it with a software known to work like "hello world").
Good-luck