Using the Possessive with Gerunds: appreciate their thinking or appreciate them thinking?

In formal writing, which sentence would be a better choice to imply "I appreciated that they had thought of me"?

1. I appreciated their thinking of me.


2. I appreciated them thinking of me.

Is there a subtle difference in the two constructions? To mean that sentence number 1 stresses on the act of thinking and sentence number 2 stresses on the people who are thinking? Or can both be used to mean the same thing?