{b} I see the difference easily enough, but I think I'd need to get a pretty good word study going before I could pick a preference (see how it's used generally, see how John uses it, etc.) In the english dictionary, it's almost circular: propitiation > atonement > expiation. They all concern atonement. ιλασμος in the dictionary in the back of my GNT is "means by which sins are forgiven". It seems that the two words differ in that propitiate's slant is to regain favor, while expiate's slant is appeasement. I'm sure plenty of study could be done here.

{c} Though I don't know ποιουμεν, it sure looks like a first person plural verb and αυτον is accusative singular ('him'), so "we are making him" seems best to me. I can't find where my beloved NASB came up with "ourselves"! :)

Last quick thoughts:

• neither translation picks up on the plural αμαρτιας as sins. I'm not sure why.
• I have a lot to learn.

RSV

• [1:7] but if we walk in the light, as he {a} is in the light, we have fellowship with one another, and the blood of Jesus his Son cleanses us from all sin.
• [1:8] If we say we have no sin, we deceive ourselves, and the truth is not in us.
• [1:9] If we confess our sins, he is faithful and just, and will forgive our sins and cleanse us from all unrighteousness.
• [1:10] If we say we have not sinned, we make him a liar {c}, and his word is not in us.
• [2:1] My little children, I am writing this to you so that you may not sin; but if any one does sin, we have an advocate with the Father, Jesus Christ the righteous;
• [2:2] and he {a} is the expiation {b} for our sins, and not for ours only but also for the sins of the whole world.

NASB

• [1:7] but if we walk in the Light as He Himself {a} is in the Light, we have fellowship with one another, and the blood of Jesus His Son cleanses us from all sin.
• [1:8] If we say that we have no sin, we are deceiving ourselves {c} and the truth is not in us.
• [1:9] If we confess our sins, He is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness.
• [1:10] If we say that we have not sinned, we make Him a liar and His word is not in us.
• [2:1] My little children, I am writing these things to you so that you may not sin And if anyone sins, we have an Advocate with the Father, Jesus Christ the righteous;
• [2:2] and He Himself {a} is the propitiation {b} for our sins; and not for ours only, but also for those of the whole world.