I suppose it depends on how you create the two sites.
If you create a.XXXX.com and b.XXXX.com under the domain www.XXXX.com
by using co-domain and directory mapping, then the statistics will be global.
The link below is how to do it:
But if you create the a.XXXX.com and b.XXXX.com separately as two entries, of course the statistics will be separated. This is logically correct.
So, why not just use Option One if you just need a global statistics ?