This is not subjective at all. You should do whatever is best for the critical components rather than what is best for the hardware overall. Some things in a computer are trivial to repair, other parts are impossible.
TL;DR: keep it turned off.
(The author of this answer has some 20+ years of experience from electronics design and repairs.)
One of the most common components to break over time are aluminum electrolyte capacitors, which you will find in any PSU old or new, and probably in the voltage regulator parts of other circuit boards around the computer. Whenever someone says that power cycling is bad, they most likely refer to the aluminum electrolyte caps (or other caps like polymer film caps), because they only conduct when the voltage is changing.
Some info about what causes them to age from a manufacturer of such components - example. Basically, they age because of voltages applied, because of cycling but particularly because of temperature. So these kind of caps definitely prefer the computer to remain turned off.
However, these are some of the easiest components to replace for someone with professional soldering experience. Don't attempt it yourself as a layman! They do hold charge for quite a long time after shutting the power off. It is also important to find a replacement part with equivalent specifications. But perfectly doable for someone with a bit of electronics knowledge.
What's nasty with aluminum electrolytes is rather that when they fail, they either do so by leaking goo all over the circuit board, or worse: fail spectacularly with a loud bang and smoke. You can avoid this if make it a habit to inspect aluminium electrolytes on a regular basis - if they start to bulge, they need to be replaced and you shouldn't power up the device until they are fixed.
Other common components likely to break are diverse forms of memories, various PROM. These come with a best before date - there's something known as data retention which is memory aging characteristics over time. This too escalates in heat.
When memories fail then that's far more severe - there's nothing you can do - the equipment is toast. (Except maybe scavenge an identical part from another device of the same kind.) The company who had the firmware for it is likely gone and they likely have no interest in keeping very old firmware around, let alone to help random collectors of retro stuff.
A PROM manufactured in the 1980s could have something like at most 10-20 years specified data retention across a temperature range up to either 70°C or 85°C. Meaning that they guarantee that the memory will stay valid for x years if you keep it below the specified temperature. Now of course we don't keep parts in a continuous heat of some 70°C, but much cooler, which is why some of these parts still work even though they are well beyond the specified data retention period. The most likely heat source is the computer itself while turned on.
Data retention is for sure a ticking bomb for all of these parts, why hobbies like collecting old video games are doomed - the only thing you know for sure is that the item will eventually fail. Could be today, could be in 10 years from now. The best way to fight it is to keep the part cool - you don't need freezing temperature, room temperature is fine, a cold basement even better. Don't leave it standing in the sun etc.
Less critical parts which are likely to fail over time are electro-mechanical parts: connectors, solder joints, cable assemblies. These definitely like the device to be turned on - a bit of current across such parts helps a lot against oxidation. However, these are also some of the most trivial parts to repair. And if they were assembled correctly back in the days, they are unlikely to cause problems even some 40 years later.
Also keep in mind that old electronics have horrible protection against electrostatic discharges (ESD), so while keeping the part dry is nice, this can also be problematic because dry air means more ESD. So if you are running the device, moist air is not necessarily a bad thing. Professional electronics assembly halls usually have air moisturizers for this very reason - it's more important to avoid ESD than to keep the parts dry.
Dust is obviously a problem too over time especially when fans are not running. A computer left turned off is likely to gather more dust on circuit boards etc. It's risky business to clean old circuit boards - just touching the boards with your fingers is a bad idea to begin with. A rule of thumb is to always touch the metal chassis first before touching anything else. You have to avoid using textile rags etc since they might cause ESD. You can buy an "ESD brush" which is basically a brush which doesn't cause ESD. For cleaning any form of mess on the board like leaks from old capacitors, use isopropyl. Water is also relatively harmless to use actually, but obviously you should never power up a device while there's water present on the circuit boards.
As a summary - it's better for some parts to be turned on and worse for other parts. But the common culprit degrading the most critical components - memories in particular - is heat. Electronics are therefore best stored cold and dry. Since all such devices produce quite a bit of heat when turned on, it is better to leave them turned off. Ideally store them in a cold basement or similar.
