You could ask for the route table and see what the default route is, that would tell you to some degree of accuracy what the active connection is.
This obviously has a lot to do with how you define 'some degree of accuracy'. Generally the main internet connection will also be the default route. I'm assuming you also want active connection to mean 'internet connection'.
netstat -rn
Routing tables
Internet:
Destination Gateway Flags Refs Use Netif Expire
default 192.168.0.1 UGSc 22 14 en1
so for me, my default route goes out the en1 interface. I think you need to be a lot more specific on what you mean by 'active/current' means to you.
CAVEAT: just because my default gw is on en1, does not necessarily mean that's where all my inet traffic goes. (it happens to be true in my case, but don't count on it as truth, but would probably be correct more than half the time).