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All of those things. Budget isn't massive, nor is the room. Ultimately I'm not an audio connoisseur, but if one option is better than the other I'd opt for that.
Volumio on raspi has cost me the same £30 as a Chromecast, but can also play from a hard drive or internet radio, and integrates natively into my smart home hub interface.
With raspi i can get a DAC hat and run it directly to active speakers, or a DAC+amp hat and run it to passive speakers, I'm just curious to hear why one would opt for active vs passive speakers?
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ok got it. So I guess active speakers offer you an amp that is matched to the speakers and is typically cheaper (if buying new) than separates, but you sacrifice additional input channels and maybe power. They're also (usually) less clutter. It really depends on your budget and if you want to add more sources in the future.
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Active speakers can make the most of amplifiers that are almost directly connected to the speaker and matched to the resistance of the driver+wiring. In that way a well designed active speaker can use amplifier power more effectively. If it's well designed it should outperform the speaker+amp combination.
Passive + Amp means that the speakers still work if the amp stops working, you can tailor the amp power and flavour to suit your budget etc. The amp can get very hot and use massive heat sinks because it's not constrained by the speaker box.
Those are some basic differences.
What is the constraint? Budget? Room size? What is your objective? Great sound or cool tech? Choose speakers (or at least narrow it down to a handful you like), then amp, then source.
On the volumio I'm not sure I get why you'd use it over and above any other £30 headless DLNA client like plex on a firestick or a chromecast. Given you have to pick up a phone or tablet, you might as well open the spotify app whilst you're there. What's the benefit?