Realistically speaking, a 3x5" section of sandpaper (regardless of backing) will be just enough to touch up a knife or two that have lost the shaving edge.

If you have to restore the edge on a blade with any kind of nicks or other damage or maybe an axe that needs just a little bit more work you might as well forget the sandpaper strip. It simply doesn't work. Especially stuff like 800 to 1000 grit. That's fine abrasive, basically polishing. No good for anything more radical than that.

The real benefit of the DMT sharpening card is that it lasts a lot, lot, lot longer than any sandpaper and even though at 600 grit it's pretty fine already, the diamon coating is hard and removes metal fairly fast if necessary. And it's also pretty cheap so it's going to be more cost-effective in the long run.

The Fallkniven DC-3/4 is the same, only you get the fine polishing stone as well on the other side. Costs a little more $ but is well worth it. At least it's the real deal, not just an improvised makeshift solution. You will appreciate it in the field when you need to do some real sharpening.