I recently looked at a wide variety of these tires and did some research. The tire companies don't make this easy with their naming schemes, but here is what I found as I researched.
Pirelli Scorpion Verde and Pirelli Scorpion Zero are 2 different lines and they come in 3 to 5 different versions each with different characteristics. The Continental [...]Contact series of tires also includes multiple lines and various versions and the DWS are specifically designed for snow so you can't just compare the DWS to "the Pirelli Scorpion somethings" as the specific model matters or you are comparing apples to oranges.
"I had Scorpion Zeros and they are trash in snow" - well that specific model is designed to be trash in snow, but there are other Scorpion Zero tires that are designed for use in snow, so be specific in what you are rating before you write off an entire model line.
Here are most, if not all, of the models in the Pirelli Scorpion line of tires.
Scorpion Verde
Scorpion Verde All Season (A/S)
Scorpion Verde A/S Plus
Scorpion Zero
Scorpion Zero A/S
Scorpion Zero A/S Plus
Scorpion Zero Asimmetrico
Scorpion Zero A/s Run Flat
Even though they are all described as "all season", I wouldn't trust the base versions without the A/S (and Plus) suffix on snow as...
The Zeros are more summer/dry oriented and are all season, but the base model doesn't appear to show an M+S rating and while the tire rack site says they can work in "very occasional light snow", the pirelli page for the tire doesn't even mention snow. I wouldn't buy the non A/S version of this tire for anywhere you might expect any snow. They also come in an A/S (All Season) version that has an M+S rating and has language that talks more about snow performance on both sites. Finally, they also come in an A/S Plus version which also has an M+S rating and talks about snow, and is basically an after-market version of the regular A/S tire that is typically sold to OEMs, but there are some sites that claim that Pirelli can tweak the Plus/Aftermarket version more because they aren't constrained by the OEM deal. That particular tire (A/S Plus) has enough consumer ratings on Tire Rack to show a light green (good) rating for snow, but that appears to only include 18 entries so it could be suspect. I'd look to the A/S (Plus) versions if you value dry/wet handling more and need to occasionally drive in snow, but don't live in a heavy snow belt. Some more anecdotal evidence of their snow performance would be nice.
The Verdes are more classic All Season tires. They do have a base version (no A/S suffix) that doesn't mention snow on the Pirelli site, but Tire Rack doesn't carry them. The A/S versions of this tire do include an M+S rating and also mention snow in much the same way as the Zero A/S tires (something like "and good in light snow"). The A/S Plus version shows a green (good) rating for snow on Tire Rack with 383 entries so it is probably a good indicator. Pirelli's ratings don't show this tire as having as good performance in dry and wet as the Scorpion Zero A/S, but it has good ratings there and better efficiency. The Verde A/S Plus version is rated 10/10 for efficiency/mileage while the Zero A/S Plus is rated 9/10.
I'd say that you should only look at the A/S versions of these tires if you care about snow and preferably the A/S Plus as that is the version that represents Pirelli's best take on an All Season tire not constrained by volume contracts. The Verde A/S Plus is more likely to have good snow traction than the Zero A/S Plus but there isn't enough data in the Tire Rack ratings to confirm this and the language about their snow capabilities is similar. The Zero A/S Plus has better wet and dry ratings than the Verde A/S Plus on both Tire Rack and the manufacturer web site.
As far as Continental DWS06 vs Scorpion Zero/Verde A/S Plus - all 3 have a light green (good) rating on snow, but numerically the DWS06 are a little higher than the Pirellis (7.8 vs 7.3/7.2) and the DWS06 have the most consumers rating it at 900. Based on the ratings I'd trust their snow capabilities more than the Pirellis, but they still lag behind dedicated snow tires.
I went with the Zero A/S Plus as I live in California and only get into the mountains once a year or every other year or so and wanted to stick with stock sizes and load ratings. If they ever up the load rating on the DWS06 front tires then I'd consider it as well.