I've been on Michelin AS 3+ for 3 years and they are amazing tires in dry, rain, cold, and light snow. Meh in snow but I've had cars in the lake effect world....you get used to how to not overdrive a car. That being said, the AS4 and dws06 plus are new. The former seems to have a much better tread pattern for snow, in particular directional and stopping issues, and the latter has a better compound.
In doing recent "research" I came across a "tyre reviews" channel on Youtube who tested at the Michelin testing grounds the AS4 lapped 6 seconds faster and stopped way better than the other 6 UHP a/s tires....the dws 06 (not plus) was in that mix. I don't think the new "plus" conti will get 6 seconds...
Since I am a suspension and handling guy, I am going with the Michelin AS4's soon. If I lived in say a place with more snow I might go conti but probably would just get a second set of wheels and go alpin's.
I have had Continentals in the past and Michelins.
Continentals for me have lasted a little longer scaled for tire rating on the same cars... I rotate q5k miles and have alignments that are kind to tires on purpose.
Both brands have good warranties and seem well made. The Michelins for the last 3 sets of tires on different cars have had one special feature, when road force balancing them, they have not needed any weights at all. I find that remarkable q/c. For that reason, I am biased from the get go to go Michelin.
Here is a link to that YouTube video on 2021 UHP tires.
(I have nothing to do with this person, just a decent review)
The guy forgot the BFG and did not have the newest Conti, but the results for the Michelin are remarkable...that is where I am going.
I run 18's on my 2019 STI and prefer the extra sidewall and increased tire selection...
Good luck to the OP. My vote is the Michelin AS4 and that is how I plan to spend my hard earned dollars in about 7 weeks.
Note, the michelin are 3 pounds heavier than the conti...but that is probably all sidewall....the loss of directional input/feel on the dws, based on dws06 v as3+ that I have actually felt on the same car, was noticeable to me and I far prefered the feel of the michelins. For a person who has done a few laps around a track, it is a big deal. But I wish the Michelins would go on a slight diet too. The Michelins are wider and "might" protect the rim a tiny bit better (not sure on this).