I can change things but will only do that when all you mathematicians have some agreement about it ...
Otared points out that the distinction between \triangle and \bigtriangleup comes from plain TeX. plain.tex has these definitions: \mathchardef\triangle="0234 \mathchardef\bigtriangleup="2234 So \triangle is a math ord and \bigtriangleup a math bin. For compatibility, that should probably stay true in ConTeXt too---even the low placement of \bigtriangledown, which I don't understand but which does reproduce plain TeX's placement.
Btw, it is still on my agenda to provide a mechanism for switching between math dictionaries (i.e. group symbols in group switch if needed different properties) so that one can switch between logic, statistics, streetfighting or whatever math.
Hm, like different dialects of a language. Plain TeX definitely speaks a pure-mathematician dialect. It would be interesting to see what symbol groups are useful in other dialects. -Sanjoy