The letter reads:

To the Dark Lord

I know I will be dead long before you read this
but I want you to know that it was I who discovered your secret.
I have stolen the real Horcrux and intend to destroy it as soon as I can.
I face death in the hope that when you meet your match,
you will be mortal once more.
R.A.B.

So, from this letter alone, we know that R.A.B.:

Was a follower of Voldemort, since he addressed him as Dark Lord.
Discovered Voldemort's secret(most likely that he was trying to make himself immortal through the use of Horcruxes.)
Knows he will die, and is facing death in hopes that Voldemort will be mortal when he meets his match(Harry Potter.)

What we know about Regulus:
Joined Death Eaters because he agreed with their philosophy.
Found out that they were prepared or preparing to go farther than he thought(most likely Voldemort making himself immortal.

Regulus could have gotten and destroyed the Horcrux (or not destroyed it) before he was killed, which was probably how he was facing death.