There's an interesting discussion between Christine Denniston & Alberto Paz here:
http://groups.yahoo.com/group/tango-uk/message/5436 which deals with the 2x4 transition to 4x8.
In the end, what matters is how the musicians play the music, and how it is heard. The notation is secondary, and it serves the music and is not its master. Nevertheless, in principle, different metres are not interchangeable: they imply particular basic patterns of stress. It doesn't make any difference at all what length of note the basic pulse is determined by, be it quaver, crotchet or minim (sixteenth, eighth or quarter note), what matters is how they are grouped into bars.
Two, of anything, gives the basic pattern of STRONG, weak. So 2/4 gives the simple march time, but while music may be notated that way, it needs to be written and played in such a way that it is felt that the bar does divide into 2 crotchet beats. The metre has determined that the crotchet is the basic pulse (and the tempo, where indicated, will be in relation to that beat length), but where the actual notes are all, say, quavers, and the music is being felt in 4, the arranger of the musical score has broken a basic rule, whether out of convenience or expediency, and the music is really in another metre altogether, because the underlying unit of pulse has changed, and the stress pattern implied by the chosen meter is not actually present.
There is no need, musically, to use common metre (4/4 or 4/8 at all, unless you intend to convey a different expectation about how the music will be played. If 2/4 and 4/4 are interchangeable, one of them serves no purpose, and needn't exist. I well remember my own music exams, where we sat, learning to notate music from hearing it played. It was the most stressful part of the exam, too. The teacher would tell us the key, and play the tonic chord to establish the pitch. Then he would beat time with the palm of his hand on the top of the piano to establish a basic pulse and rhythm pattern, for a few bars, and then he would play a simple piece of a few bars, repeating it several times with pauses in between, and we would notate it. Woe betide anyone who made the basic mistake of not even getting the note lengths right, and grouping them properly. If I remember correctly, the range was limited to simple metres of 2 3 or 4 beats, and 6/8, the simplest compound time (where two groups of three made one bar, rather two).
There seems to have been a convention, in early tango notation, to play with a pulse that is twice that indicated. The 2x4 pattern that was so common before the Golden Age (but which survived in milonga, later) was based on a quaver pulse (eight beats over two bars).
'ONE two | three FOUR | FIVE six | SEVEN eight' fits into four bars having a STRONG, weak rhythm perfectly (allowing for the distinctive syncopation reversing the stress in the second bar). However, by convention, this was written in 2/4 with a quaver pulse, but
my teacher would have corrected my work, and gently suggested writing either in 2/4 with a crotchet pulse, or possibly 2/8 with a quaver pulse.
Later tango, written in 4x8 has the pattern:
ONE two THREE four | FIVE six SEVEN eight, with regular stress on alternate beats, and common time (4/8 suits this perfectly. The quaver pulse is carried over from the earlier convention, but the groupings of beats now follows the metre being used to express them.
All this is pedantry, and I remain content to be in a minority of one. If I
am wrong, no one has shown me where...