Until it can be proven that John Kerry refers to his war record to defend everything he says as often as Bush refers to 9/11 to defend every policy decision he makes, I'm going to have to say that Kerry hasn't made his war record a key issue as much as Bush has. I could be wrong. Maybe Kerry's just using his connection to the Vietnam war and his protests against it to try and get in a double-deal of support from current troops and from people against the Iraq war.
But for now, I don't believe that Kerry's running on his war record. I believe the Bush administration is trying to focus only on John Kerry's war record, saying that's all he has to go on, and the media plays along because it makes it easier to produce soundbites. The Bush campaign is trying to bamboozle everyone by making us focus on national security and the "war on terror" instead of on all of the domestic issues like the economy and social issues like gay marriage. This is because Bush has a lot lower approval rating on domestic issues, but a higher approval rating on security.