The standard advice on a second camera is to buy the same model as your first, so that everything matches and either can be the main body.
I did the opposite, partly by accident, and have come round to thinking the accident was right.
What a second camera is actually for
Three distinct jobs, and matching only helps with one of them.
Insurance, if the main body fails. Here matching genuinely helps, because you can continue without any change to the workflow.
Multi-camera shooting, where both run simultaneously. Matching helps with colour consistency, though it is not essential and is manageable in the grade.
And doing something the main body cannot. Here matching actively hurts, because two identical cameras have identical limitations.
Which of those is your actual need determines the answer, and most people assume it is the first without checking.
The case for a smaller one
My second body is considerably smaller than my main one and it has changed what I shoot more than any other purchase.
It fits in a bag I carry anyway, which means it is present in situations where the main camera is at home. A substantial amount of the material I value most came from having a camera when I did not expect to need one.
It is unobtrusive, which matters for documentary work and for filming people who become self-conscious around a large camera. The behaviour you get in front of a small camera is different, and often better.
And it goes places a large camera does not. Mounted in a car, on a bicycle, in a confined space, somewhere a large body is physically awkward.
The case for a differently specialised one
The other direction. A second body chosen specifically to cover the main one's weakness.
If your main camera has poor low light performance, a second body that is strong there expands what you can shoot.
If it has no high frame rate capability, a cheaper body that does gives you slow motion without replacing anything.
If it has a limited recording duration, a second body without that limit covers long events.
Each of these turns a limitation into a solved problem for less than the cost of replacing the main body with something that does everything.
Where mismatched bodies hurt
Being fair about the cost, because it is real.
Colour. Two cameras from different manufacturers render colour differently and matching them in the grade is genuine work. It is doable, particularly if you shoot a colour chart on both at the start, and it is not free.
Menus and controls. Switching between two different interfaces under pressure produces mistakes. I have set the wrong frame rate on the second body more than once because the setting lives somewhere unfamiliar.
Batteries and media. Two systems means two sets of everything, which is weight, cost and one more thing to forget.
Lens mounts, if they differ, which is the largest cost of all and the one that would make me reconsider.
The practical mitigations
Shoot a colour chart at the head of every setup on both bodies. Ten seconds, and it turns matching from guesswork into a procedure.
Set both cameras to the same white balance manually rather than automatic, so they do not drift apart during a take.
Match the picture profile as closely as the two allow, and if one shoots a log profile and the other does not, use the flattest available on both.
And write down the settings for common situations, taped inside the bag, because remembering two menu systems is not something to rely on.
What I would not buy as a second body
Something significantly worse in every respect, bought purely on price.
A camera that is worse at everything gets used only in emergencies, which means it sits in a bag depreciating and you are unfamiliar with it when the emergency arrives.
A second body earns its place by being used regularly, which means it has to be good at something. If there is no situation where you would choose it over the main camera, it is not a tool, it is a spare part.
The order I would buy in
If the honest need is redundancy for paid work where failure is unacceptable, buy the same model or rent for those jobs. Matching wins.
If the honest need is capability, buy the thing that covers your gap, accept the matching work, and use it constantly.
And if you are not sure which it is, it is probably the second, because true redundancy needs are rarer than people think and are frequently better solved by renting than by owning.
The insurance question, honestly answered
Worth closing on this since it is the reason most people give.
In about nine years I have had one camera fail during a job. It was a card slot rather than the body, and the fix was a different card.
Which is a sample of one and not an argument. What it suggests is that the probability is low enough that carrying a duplicate for that reason alone is expensive insurance against a rare event.
Rental is the cheaper form of the same cover for anything genuinely critical, and it has the additional advantage that you can rent exactly what the job needs rather than whatever you happened to buy.