The difference is the power differential: at the time Apple ran those ads, they were much smaller and semiregularly the topic of speculation about bankruptcy. Pitching them as better than the dominant platform was trying to get buyers to think of them as peers.
In this case, Intel has been the dominant player since the 90s, possibly the late 1980s in the consumer market. Running an ad saying they’re afraid of a newcomer’s first product (in this segment, of course) seems different because they’ve been a safe default option for decades - especially because this option was created to replace their products. It seems just as likely to make consumers wonder why they’re so worried about.
As opposed to this ad that uses PC and Mac??? I don't get your argument when it is basically the same argument inverted. This advert doesn't include prominent Intel branding either - they are fighting for the PC segment.
Apple did literally the exact same thing back in the day, saying some programs don't work very well on PC and urging people to get an Apple computer. Check out one example:
PC isn't a brand. Apple was referencing all non-Mac computers (not just Dell or HP) as their competitor. Intel is specifically referencing a single chip from a single competitor.
If the Apple ad said "Mac is so much better than the Dell XPS", that would be different.
M1 Mac is three different computers; Intel is taking a swipe at Apple Silicon in general. They want Apple to use Intel chips for refreshes on the bigger devices (MBP16 still ships with 9th-gen Intel, iMac with 7th-gen). Anything they can do to delay Apple Silicon market takeup will dampen the attractiveness of post-M1 models running Apple Silicon, because nobody wants a machine with sparse software availability and that's a problem that won't get resolved until the user base is much bigger.
At the time of "I'm a Mac, I'm a PC," Apple transitioned to Intel. Now that it's transitioning away from Intel, you're seeing the same argument but inverted.
Sure, “PC” was (is?) synonymous with Windows, but as @ricketycricket said, Apple wasn’t calling out a single thing, but all computers that are labeled “PC”.
In this case, Intel has been the dominant player since the 90s, possibly the late 1980s in the consumer market. Running an ad saying they’re afraid of a newcomer’s first product (in this segment, of course) seems different because they’ve been a safe default option for decades - especially because this option was created to replace their products. It seems just as likely to make consumers wonder why they’re so worried about.