The difference is that the german tank sample can only be drawn from the pool of existing tanks so far. But when you consider your own birth, that's a sample out of the pool of all the humans, including future ones. Because future humans can also ponder their own place in the sequence, and where they find themselves is distributed uniformly over the sequence of all humans.
To apply the doomsday argument to tanks, we need to fix the sampling. It won't work for allies grabbing german tank samples. We have to think from the point of view of the tank; say a copy of your consciousness is being uploaded to an army of tanks. If you wake up as tank #734, could there eventually be millions of tanks? Maybe so, but there's only a 5% chance that you are one of the first 5% tanks, so there's a very good chance that there will be less than 734*20 tanks in total.
To apply the doomsday argument to tanks, we need to fix the sampling. It won't work for allies grabbing german tank samples. We have to think from the point of view of the tank; say a copy of your consciousness is being uploaded to an army of tanks. If you wake up as tank #734, could there eventually be millions of tanks? Maybe so, but there's only a 5% chance that you are one of the first 5% tanks, so there's a very good chance that there will be less than 734*20 tanks in total.