It depends, it really does. One of the local aviation companies I got to tour had two processes- one for SMD (mostly automated) and one for THT (mostly soldered by hand). On the newer SMD processes, the most popular computing chips were Xilinx FPGA's, which were
everywhere. The way it was explained to me was that the FPGA can handle
internal redundancy [1] without any additional space cost, and that one of the main reasons that they used FPGA's was that it makes it a lot easier to handle backwards-compatibility with older stuff. Another reason FPGA's are so useful is that they can cram a lot more calculations into less space, making the entire unit more compact. [2]
With that out of the way, yes, missiles now have a lot more computing power in them, even if they do more or less the same job- accuracy is generally the thing that improves here, as the physics models can be expanded to be more correct, as the number of sensors, and the way they are combined evolves, the end result is a better product. (And more Defence money, to boot!)
I've gotta say one more thing, though- a lot of the stuff in the military, and that goes to it, is built off now-ancient processes, because A) contracts, B) If it works, don't fix it, and C) standardization, so you may not see an FPGA in every missile, but they're getting there.
[1] this doesn't count as far as redundant parts are concerned, but it does give the engineers (and, by proxy, the customers) more trust in the outputs from the devices.
[2] It also costs way less space (and therefore money, to some degree, because mil-spec enclosures are expensive), to get two 1U servers than it does to have one vacuum-tube operated mainframe.