Yes, they're both the same, it's just that the LM393 is an 8 pin version and if he wants a compact solution, there'd be no point in using the 14 pin version, since he'd only be using on quarter of the IC anyway.
Typical capacitors hav an accuracy of 10%, especially in the value range required to give a 1Hz output.
I think a PIC and crystal is probably the best option, the only advantage the counter has, is you don't need to program anything.
Jack,
What do you need the 1Hz reference for?
Surely there are other elements you could integrated in to the MCU?