If you are proposing Pigovian taxes, then both make sense but address very different things. Driving a car imposes external costs through the impact on the environment, through the wear and tear on the roads and through the time cost of congestion.
A mileage tax addresses the wear and tear issue. People who drive will be assessed a tax that is equivalent to the cost of the road wear they are responsible for. This has the benefit of being fair and providing a direct source of funds to maintain the roads and is a disincentive to drive once the external cost is made internal through the tax (and also taking into account the cars weight, etc. - of course how will they deal with studded tires and chains?). The implementation is costly however, having a GPS in each car has got to be expensive as well as the cost of reading them and imposing a tax. Perhaps we could just do a mileage charge - not as accurate but simple.
The mileage tax does not address the congestion issue, but with the GPS it could, one assumes. If you drive on certain congested roads at certain rush-hour times, you could be charged more. This would provide the same Pigovian incentives to avoid driving during rush-hour or in congested areas. The GPS could also determine how much tax should go to municipalities, counties, and the state depending on which roads you drove on. But doing these things would seem to be an enormous computing challenge and one that would be enormously expensive. It is an interesting idea, however.
The gas tax is Pigovian in addressing the environmental impact of the amount of carbon emitted which is exactly related to the gas used. If the primary goal is to address this than this is the appropriate tax.
It is clear that each tax is also a poor way to address the other issue, to wit: a gas tax is not a good way to address wear and tear because a Prius could do a lot of wear and tear with little gas and a Mustang could do little wear and tear with a lot of gas; and a mileage tax doesn't work, for the very same reason, as a way to address environmental impact.
Both taxes could be implemented, but since the gas tax is good for the environmental impact side and, though imperfectly, does address the wear and tear side as well, and is basically zero extra administrative cost, it seems like the clear winner. However, if the GPS system could be done very cheaply and has the added congestion and differential tax components, it might be worth pursuing. Perhaps it is politics but I don't see what's wrong with a healthy increase in the gas tax - besides the GPS monitors will just serve as a constant reminder of the government's taxation which will fuel the anti-tax sentiment latent in almost everyone.
Note: One thing I failed to mention is that the milage tax is imperfect in that non-Oregon registered cars that drive in Oregon (for example, Vancouver commuters) would get off scott-free. At least a simple gas tax would catch some of them and would work both ways (Oregon drivers in Washington would pay for Washington's roads only when they buy gas in Washington).