Analog computing sucks. It's inherently sensitive to noise and random variation in your devices that's basically ubiquitous with modern chip-making processes. Digital electronics actively reject noise at every step in a computation, albeit at the cost of wasting energy in the process. With analog, a more complex computation becomes exponentially harder.
There are forms of analogue computing beyond solving DEs with circuit theory. One of the more esoteric examples I'd heard of was using DNA microarrays for massively parallel SAT solvers: combinatorically generate a very large number of different, long single-strands of DNA using clever chemistry, flow over short pieces of DNA that encode your problem that are flourescently labelled, and then "simply" read off the result. Being able to use the fact that Avogadro's number is absolutely massive is a big speed-up for some particularly nasty NP-hard problems where you want to brute force it.