So given a choice between a non-resonant length of wire antenna center fed by 50 Ohm coax, or a resonant length of wire fed highly off-center by 50 Ohm coax, or a resonant length of wire fed by high impedance open twin lead, and with no matching networks of any kind either way, what would be the difference in advantages or disadvantages, if any?
All these options are bad. It's a bit like asking if it's better to drive a nail with a floppy shoe or a glass jar.
If you really had to make a decision between these contrived options, you'd have to flesh out the details to make a decision. There are a few things to consider.
Firstly, a half-wave dipole may have a substantially different radiation pattern from some other length of dipole. Or they may be substantially similar. One may be better or worse for your application.
Secondly, any mismatch is going to cause additional loss in the feedline. How much loss will depend significantly on the details, like the reflection coefficient, the length of the line, and so on.
But I suspect what you're really asking about is my answer to Does a resonant antenna work better than a non-resonant antenna?
The situation of a non-resonant antenna is similar in many ways to a resonant antenna with a mismatched feedline. In either case, the feedline will operate at an elevated VSWR and this will increase losses.
But there are differences as well. A resonant antenna will have a purely resistive impedance, by definition. This means there is theoretically some feedline that will match it, even if that feedline isn't available or practical to construct.
But a non-resonant antenna will have non-zero reactance. While the characteristic impedance of a feedline can also include a reactive component, and so maybe there's theoretically still some feedline that could achieve a conjugate match, that means the feedline is lossy. Making a feedline deliberately lossy to achieve a better match to reduce losses doesn't make any sense.
Finally there are also losses in the antenna to consider. For example, a very short dipole becomes more like a capacitor than an antenna. Significant current will go towards charging and discharging that capacitor while relatively little goes towards radiation. Of course this will mean additional losses in the feedline as previously mentioned. But it will additionally mean higher losses in the antenna itself.
Non resonate antennas used with out match networks, usually an antenna tuner, will result in high VSWR and low efficiency.
For receivers you can use them without many problems. They will not be able to receive very weak signals, but other than that they will work.
The issues become much greater when you transmit. The high VSWR causes voltage feedback into your transmitter which can damage the final amplifier. There will almost always be some mismatch between the antenna, feed-line, and transmitter, but you want to minimize it.
The mismatch also results in less of the transmitter's power actually being converted into RF signals.