Its not quite apples to oranges as many of the dangers of aspirin (e.g. stomach ulcers or liver damage) are due to long term exposure or over dosing, neither of which can easily happen with a vaccine.
I can’t make sense of what you’re even trying to say:
1. That the mechanism of harm is different tells us nothing about the relative risks. I don’t OD on cars, but cars are riskier than Asprin.
2. You can have long term negative impacts from, eg, vaccine carriers. (Which is why we stopped using some....)
3. Overdosing a live virus vaccine happens all the time, the result being you get the illness. A flu shot can kill you by giving you a deadly flu.