Hello Marshall,
Each interrupt source enable on the LPC925 (in all but the very early 80c51) has associated with it two bits that control the priority for that interrupt. This gives the ability to set any interrupt source to one of 4 priority levels so that it can be promoted and serviced ahead of others.

You can test this by setting up T0 and T1 to interrupt together, but promote one (say T1) to a higher priority. It will always be serviced ahead of the other.

When interrupts from multiple sources occur together the arbitration scheme comes into effect which is simply the polling sequence.

If you ran my suggested test code without altering the priority level you would find that T0 will always be serviced ahead of T1.

Hope this clears up your confusion.

Phoebe