The short answer is that obviously the default should be user-selectable.
My personal preference would be a cross transition,
but only if it is correctly implemented.
Currently the choice offered is between a buggy cross transition, or a correct overlap transition that moves clips. Not a good choice. Don't let's allow the choice offered to conceal the actual problem.
Now for the longer answer - sorry to ignore the request in the original post, but it's essential that the full picture is taken into account.
First - in a properly edited video
there need be no difference between the outcome of a cross transition and an overlap transition. The difference is not in the end result, but in the means used to arrive there. It's all in the trimming style you prefer.
Unfortunately there is a fatal flaw in the PD9 cross overlap programming, such that there is
always a difference in its cross and overlap transitions. This is a serious problem at the heart of the program.
Overlap transitions in PD9 are true transitions where all the motion seen in the clips involved continues throughout the transition. If the edit involves two clips of a man walking along a road, throughout the transition you see him continue to walk.
Cross transitions in PD9 are not true transitions, but are implemented using frozen frames, so that in the same example of two clips showing a man walking along a road, at the point where the transition begins you see a man standing frozen in mid-pace fading in, as the image of a moving man in the first clip fades out. At the middle of the transition you see the the image of the fading out man suddenly freeze in mid-pace, while the fading in man suddenly unfreezes and is seen walking along.
Such a transition should never be seen in other than beginners' videos as it is normally symptomatic of the editor not understanding how to construct a proper cross transition (use of untrimmed clips, see following). Of course if there is little or no movement in the shot (or it's a still) or the transition is very short the fault may not be evident, but otherwise it's likely to be obvious and jarring.
A properly functioning cross transition works like this. Assume that the total transition length is two seconds. The two clips are first each trimmed by the user by at least one second (half the length of the transition) at the point where they are to join. Then they are butted together and the transition is dragged across the join. Internally, the program then extends the length of the first clip by one second to the right (using the frames following the end of the trimmed clip) and extends the length of the second clip by one second to the left (using the frames preceding the beginning of the trimmed clip). The result would visually be the same as an overlap transition (using clips not trimmed for the transition), except that the clips remain where you've placed them, not moved to accomplish the necessary overlapping frames.
A properly functioning cross transition also has to take into account what must happen if the user does not understand how to work with a cross transition, and who uses untrimmed or insufficiently trimmed clips. In that case, there may be insufficient frames available after the end of the outgoing clip, or before the beginning of the incoming clip, to extend the clips as described in the preceding paragraph to form the necessary overlap. So, there is no option other than for the program internally to repeat the last available frame in the outgoing clip, and/or the first available frame in the incoming clip, enough time to provide material for the transition. This leads to frozen motion of course - it's a "freeze frame".
Unfortunately in PD9 the developers have seen fit to assume that the user will always be ignorant of how to construct a cross transition, and the transition is therefore always created by repeating the last yrimmed frame of the outgoing clip, and the first trimmed frame of the incoming clip, each for half the length of the transition, leading to the unacceptable frozen motion described earlier.
SO - right now, if they provided the obvious user preference for default cross or overlap transitions, they might have to label the options thus -
Cross Transition default - this will cause frozen frames during transitions
Overlap Transition default - this will move the clips on the timeline by the length of the transition.
If however they implemented true, usable cross transitions, then the options might then be labelled (notionally)
Cross Transition default - this requires you to trim your clips to provide enough material for the transition to be created
Overlap Transition default - this will move the clips on the timeline but you don't have to trim the clips first.