Found a paper (a bit older, 2001, but should still be mostly accurate) comparing the two. Cliff notes:

• Despite legislative power going by default to the central state in Spain and to the states in Germany, distribution of power is overall comparable. Less uniform in Spain as every region gets its own autonomy statute instead of all German states pooling their sovereignty in a uniform way.
• Administration is practically completely state matter in Germany, while Spain retains central administration structures in all regions. Those largely delegate matters to the region’s administrations, though. So again overall not too dissimilar in practice.
• Regarding the judicature: The regions don’t have courts. They have some say when it comes to how court districts are drawn and that’s pretty much it. German states all have their own courts and appeals courts, the federal level only has cassation courts. In this area German states have way more autonomy. States elect judges for their own courts as well as 50% of federal judges, or 50% of the people who elect them are designated by the states, depending.
• Spanish regions have very limited means to influence central legislative. No right to initiative, no own legislative body, just a right to petition. German states can initiate federal law, have their own legislative body, and much federal law needs passing by both federal and state bodies because it tangentially affects state prerogatives.
• Interestingly, the federal level has larger powers of oversight over the German states than Spain does over the regions. In both cases the oversight isn’t large, though, in Germany it only exists in so far states are administering federal law on behalf of the federation, which isn’t often the case. E.g. (practically all) criminal law is federal law, but administered by the states on their own behalf.
• German states have more financial autonomy. I won’t get into details the distribution of taxes between federation and states in Germany is complex AF, also, has been renegotiated multiple times. Regarding administration, though, as said: The federation has no tax office, they couldn’t collect taxes if they wanted to.
• German states have much, much, much more power when it comes to asserting their power. Maybe that’s why they’re not as hell-bent on carving out power for themselves: Autonomous regions have to rely on public sentiment and the good will of the constitutional court, otherwise the central authority can just walk straight over them, so they take whatever they can get their hands on while German states are much more relaxed about it.