Where to put a voltage (DC/DC) converter that must be switched on/off by the control signal?
Even with a bit of unknown in your system spec requirements, here are my thoughts.

You mentioned 2 ways to control the load power rail:


On-off switch upstream the DC-DC converter (switching Vin)
On-off switch downstream the DC-DC converter (switching Vout)


I would add one more:


Controlling the DC-DC converter on-off state through a built-in Enable or Shutdown input


For #3, you most likely need to design your own DC-DC converter circuit choosing a part that has the enable/shutdown logic, it looks like this is not an option for your setup. In any case, this solution has many advantages like:


not adding external control circuit
re-using the soft-start feature to "gently" power-up the load (most DC-DC converters come with it)
very-low quiescent current when shut down


For #1 and #2, you've already mentioned the pros and cons of both solutions so let me suggest a simple implementation :)

If you can integrate it into your circuit, high-side switching can be done using a combination of N-channel + P-channel MOSFETs that should work beautifully.
Have a look at this post:

High Side Switch Implementation (Active-High)

The "control" line would be wired to your 5V logic.

For the upstream option, wire the "5V-input" to your 5V rail and the "5V-Switched-Output" to the DC-DC converter Vin (voltage input). When "control" is high (eg. above the N-channel Vgs turn-on threshold, between 1 and 2.3V for this FET), the "5V-Switched-Output" will be connected to "5V-input" and feed the 5V rail to the DC-DC converter. When "control" is low, the "5V-Switched-Output" will be disconnected from the "5V-input" therefore the DC-DC converter will start to starve and its output (12V) will go down to ground.

For the downstream option, it will have the exact same logic except you would need to connect the "5V-input" to your DC-DC converter output (12V). The FETs used in this circuit will still work at 12V, both their Vds and Vgs can support up to 30V and 20V respectively.

Now there are a few things you should have in mind:


however dependent of your 5V and 12V rail capacitance, the switching from on to off state (and vice-versa) will be quiet "quick" (in ms). If you need a graceful power shutdown, you should probably tell the 12V device to save its context before shutting it down (if in the middle of running operations, it may power back up in a confused state)
it is true the upstream switch will prevent current draw from the DC-DC converter when turned off but we are talking micro-amperes and if your system can deal with that (eg. not battery-powered), there is nothing wrong putting the on-off switch downstream
in the upstream implementation, I mentioned you would "starve" the DC-DC converter when the switch is off which will cause its regulation logic much trouble if the Vin under-voltage threshold is too low, it may compromise your DC-DC converter reliability
the upstream switch will need to switch a higher current than the downstream switch as you have to account for the DC-DC efficiency. If your system sinks 500mA at 12V, the downstream switch can use FETs with lower currents. Now assuming your dc-dc converter efficiency is around 85%, the current on the 5V rail will be around 1.4 amps. If your system consumes even more power, you may end up having to cut-off 3-4 amps on the 5V, definitely keep this in mind when selecting the switching elements!