Good choices.

I'll go for the best

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and for the worst:

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I'll also throw in my favourite fallout song:

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There's honestly none that I dislike, though my favorites are:

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I love all the songs on the radio stations but Johnny Guitar always gets me. I love to just sit down by a campfire and listen to it when it plays on my pip radio.

JOHNNY GUITAR IS ANNOYING AS HELL.

I honestly enjoyed all of GNR's songs but I wasn't too into anything from vegas, didn't help vegas didn't have that many songs to begin with.

I'm Goin' Under, Blue Moon, Ain't that a Kick in the Head from FNV and I Don't Want to Set the World on Fire from F3 Are my absolute favorite songs, I don't hate any songs from Fallout 3 or NV, I think they fit the games they are in perfectly.

My favourite two radio songs are Frank Sinatra's Blue Moon from New Vegas and The Ink Spots' I Don't Want To Set The World On Fire from FO 3.
I can only think of one song I dislike and that's Johnny Guitar off NV, idk I just really never have enjoyed that song.

Blue moon and Johnny guitar are defineatly my two favorites from NV, as for FO3 all of the songs in that game were pretty damn swell.

It's very difficult to pick just two from Fallout New Vegas as I was very impressed with all the music, the only thing I wish is that they had more Jazz songs. However, that's an easy fix for members of this particular community.

Two Best FNV:
Ain't that a Kick in the Head - Dean Martin
Blue Moon - Frank Sinatra

Two Worst (Though I don't dislike them, just at the bottom of my like list)
Mad About the Boy
Johnny Guitar

Honourable mention - Big Iron (Go listen to the Johnny Cash version)

From F3

Two Best
Don't Want to Set the World on Fire
Anything on Enclave Radio (Yes, this counts all as one)

Two Worst (less favourable than FNV but, still don't hate them)
Wonderful Guy
Butcher Pete

From FNV i like Big Iron and Blue Moon
From F3 i just remember I Don't Want to Set the World on Fire by Ink Spots

I enjoy all musics, so i don't make a list about what i dislike :/

Big iron was my favorite song, the story it tells was inspiring and I decided to play it whenever I go into dark abd scary places like Vault 19, etc

My favorite New Vegas songs are Jingle Jangle and Blue Moon my worst is Johnny guitar I like all other songs from both games so i cant have a second worst

I don't know about official songs. Hang me, but I don't listen to the radio all to often. I'm more a fan of the New Vegas' soundtrack(s). Fallout 3 has some mentionable compositions as-well. Forgive me for I do not know the names. The soundtrack that plays in Doc Mitchell's house and the one that plays outside Freeside in the evening are personal favorites. As for 3, all of the dungeon music is awesome. IF I had to chose an actual song - "Jingle Jangle Jingle" by Kay Kyser. No dislikes for this guy. Fallout has some solid music material.

I actually really love the soundtrack of 3, specifically the Billie Holiday songs and Cole Porter's "Anything Goes" As for New Vegas, Frank Sinatra's music fit the game perfectly but "Johnny Guitar"......just no......that song led me to playing much of the game with the radio off as it seemed to come on ALL the time.