Do this time and this once mean the same? For example:
I have never allowed you to use my car but this time/this once.
If the phrases are identical in meaning, then which once is more common?
They are very similar. However "this once" implies that the event is a one off unlikley to be repeated, whereas "this time" implies the event was in doubt or unlikely but does not suggest it will be unique.
"The poker player had claimed to have a full house last hand, but this time he really did."
we are not saying anything about any past or future repetition of the event so this time we should stick to "this time". "this once" would be too specific.
"The poker player NEVER bluffed. But this once she did"
We are making the point that this is an exceptional event that should not be expected to happen again.
You can (almost?) always substitute "this time" in place of "this once" but not necessarly the other way around.