I have owned the Milwaukee Super Sawzall for around 12 years,
and the Dewalt 18V Cordless for around 7 years.
The charge on the 18V batteries don't last long enough for heavy work, and the batteries themselves need replacement after a few years. But the cord-free factor is nice.
If you go the cordless route, consider looking into the Craftsman combo. I do not know anything about their cordless Sawzall, but their 18V drill/saw combo has lasted me for around 10 years with only 1 new set of batteries required.
I had the Makita 18V cordless Drill/saw set and had one set of 2.2ah batteries that only lasted one year, and 2.8ah batteries which lasted me less than 3 years, plus the 1/2 drill burnt up at 1 1/2 years. Makita warranteed the drill and first pair of batteries.
I have the Dewalt 18V drill/light/Sawzall combo, and am looking at buying my second set of batteries in seven years.
I was in business and used these tools daily, but I think battery life would be my biggest concern if I was going to buy cordless vs. Corded. There are times where one tool outshines the other, but if I had to have only one, it would be the corded Sawzall.