Let's forget for a moment that there is no operational difference between a designer gene spliced into the victim's chromosomal DNA or transcribing off a nuclear plasmid and both could legitimately be described as "changing your DNA"...

One of the arguments the mRNA folks (BioNTech, Moderna) use for their technology is that, compared to the DNA technology (AstraZeneca, J&J, etc), their mRNA technology reduces the chances of the plasmidal DNA inserts into the cell nucleus accidentally integrating with the chromosomal DNA.  (Students of science will understand that such 'accidents' are pretty much they way we humans got here in our current form...for better or worse.)

So, you either have to claim that the mRNA folks are making up tall tales in order to sell their wares, or that the possibility exists for genuine chromosomal integration happening with the DNA vaccines in at least some accidental circumstances.  It's pretty much one or the other, and if it's the former, it is worth asking what else the mRNA folks might be lying about in order to make sales.