3 obvious benefits of having elite status with more than one carrier in the same alliance.

1) most airlines provide best treatment and best benefits to their own elites
2) utilise differences in earning and burning rates for particular routes. There are some very significant differences in rate of earning miles and cost of awards which very frequent flyers can take advantage of.
3) currently, with a few exceptions, you can only upgrade using miles/vouchers of the airline you are flying

A major disadvantage is miles earned are spread more thinly, but if flying enough this may not matter.

I'll leave others to comment on status match.