Both albums had successful re-releases. Both were very good eras for both stars in terms of fashion and image-wise. The biggest single for Beyonce was Irreplaceable which was #1 on the US chart for 10 weeks in 2007. Rihanna's biggest single Umbrella was #1 for 10 weeks on the UK chart in 2007. There were 3 main collaborations on both albums.
Rate the album tracks.

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

Too lazy for that lemme just say that GGGB is better than B'day in every way.

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

GGGB

Good Girl Gone Bad, only Irreplaceable would win with Lemme Get That and maybe Ring The Alarm with Shut Up And Drive

İ only like cry and disturbia from GGGB album.
So B'DAy

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

B'day wins it.

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

B'Day 8
GGGB 7

B'Day just wins it

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)
OVERALL: B'Day, but GGGB's best songs are better than BD's best songs.

Bday is perfection.

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

B'Day - 9
Good Girl Gone Bad - 7

Very close but I prefer B'Day. GGGB is a fantastic album as well.

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

Good Girl Gone Bad >>>>>>>>>>>>>>

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

Good Girl Gone Bad.

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)

Flawless album tbh

Deja Vu (ft. Jay-Z) vs. Umbrella (ft. Jay-Z)
Get me Bodied vs. Push Up on Me
Suga Mama vs. Dont Stop the Music
Upgrade U (ft. Jay- Z) vs. Breakin Dishes
Ring the Alarm vs. Shut Up and Drive
Kitty Kat vs. Hate that I Love You (ft. Ne-Yo)
Freakum Dress vs. Say It
Green Light vs. Sell Me Candy
Irreplaceable vs. Lemme Get That
Resentment vs. Rehab
Beautiful Liar (ft. Shakira) vs. Question Existing
Welcome to Hollywood vs. Good Girl Gone Bad
Flaws and All vs. Disturbia
Listen vs. Take a Bow
If vs. If I Never See Your Face Again (w/ Maroon 5)
This was extremely hard i love both of these albums