I doubt they will be advertising the Taycan much for a few years. Production will be limited and demand is currently high. When they do start advertising they will probably push the advantages the Taycan has over Tesla equivalents, but they have to be careful about making things up because that will come back to bite them. Few Porsche owners ever take their cars to the track, but most Porsche fans pay attention to what those who have taken the cars to the track have to say. If Porsche claims better performance from the Taycan and a Model 3P can trounce it on the track, news will get out. Though I expect the Taycan's track performance to be pretty good, Porsche does know what they are doing there.
I don't read car magazines, but I don't recall ever seeing a Porsche ad on TV or non-car magazines. Maybe they do in Europe? I've seen VW and Audi ads many times. Advertising also involves talking up the car to the car media, and they probably will be doing that.
The Taycan might end up being like the Chevy Bolt, a flash in the pan at first, then a year later they have trouble selling them. In the end it probably won't put much of a dent in Tesla sales. Production is too limited and it's too expensive for what you get. Die hard Porsche fans will declare it the best EV ever made, but the rest of the world will probably be "meh" about it.
At the end of the day it's essentially a high performance touring sedan, but it lacks both range and space compared to the Model S Performance and lacks range compared to the Model 3 Performance, and until high speed CCS becomes common, charging on the road is going to be a poorer experience than Tesla's. The price is going to be on par with a Model S Performance.