If your other children each took 3 A-levels the maximum number of UCAS points they could have achieved (by getting 3 A grades) would have been 360. (However, from this year the maximum number of points available from 3 A-levels is now 420, through getting 3 A* grades).
The maximum number of UCAS points available from a BTEC National Diploma (by getting a triple distinction) is also 360. So the UCAS system ranks a BTEC National Diploma as similar to three A-levels.
For finer detail, see the 'Diploma' column, under 'BTEC Nationals' here:
http://www.ucas.ac.uk..._tariff/tarifftables/
Compare it with the 'GCE A level and AVCE' column, under 'GCE and VCE'.
Whether the BTEC qualification would actually be useful in gaining university admission must, of course, depend upon it's relevance to the subject which your son would be seeking to study. (i.e. it's clearly useful for a sports-based course, it might help gain admission to a more general course relating to the leisure industry but it obviously would be useless when seeking a place to study, say, mathematics).
Remember that admission to Uni isn't solely based upon grades and UCAS points. A good 'personal statement' to accompany the application is also important. The BTEC course, and the sports activities which are likely to be associated with it, might put your son in a good position to submit a first-class statement:
http://www.bbc.co.uk/news/education-11023939
Chris