I love them both, but I slightly prefer ANatO. It's maths: 12 great tracks beat 10 great tracks (11 if you count the overture/finale). I'll compare them not by track order but by their respective album-to-album equivalent:
Best Friend vs You and I: The latter's got much better piano work, heavier guitars, busier drumming, but I prefer YMBF. Reason? While both have amazing harmonies, I'd give YMBF the edge thanks to the descending 'happy at home' near the end. It's just perfect.
I'm in Love with My Car vs Drowse: Car for me. More vocals, and more demanding too.
Prophet's Song vs White Man: I didn't quite like White Man until I heard it again and it's finally grown on me. But IMO The Prophet's Song is still a hell of a lot better.
'39 vs Long Away: Long Away is fantastic, but '39 is IMO the best Queen song ever so, no contest really.
Sweet Lady vs Tie Your Mother Down: They're actually quite different, aren't they? Well, in this case I would choose TYMD anyway - Roger's harmonies in particular are better there (on SL they're great but a bit less). I also prefer the bass on TYMD.
Good Company vs Teo Torriatte: Again they're very different, yet they're the 'odd' ones out. I adore Teo and it's my favourite song on ADatR. But I still prefer GC. Actually, it's my second favourite Queen song.
God Save the Queen vs Overture/Finale: They're both amazing, but I prefer the National Anthem as it's much more arranged and less repetitive. It's also more May-estic IMO.
Love of My Life vs You Take My Breath Away: They're both gorgeous, they've both got amazing vocals, guitars and melodies. But I still prefer LoML because of the piano solo, the harp and the acoustic.
Death on Two Legs vs Millionaire Waltz: They're very different, but they can be compared in terms of piano-playing skills (DoTL intro is more difficult and is played more 'choppy' than anything on TMW, but the rest of DoTL is really simple, while TMW is far more demanding without being 'complex' either). I think I'd declare a tie there.
Bohemian Rhapsody vs The Millionaire Waltz: Each is the most complex and intricate number of its parent album. I love them both, but I'll pick Bo Rhap. Why? There's no accounting for taste.
Bohemian Rhapsody vs Somebody to Love: Comparable in terms of each being the lead single. In that case, I prefer StL - it's much simpler, yet it's equally wonderful, and the triple metre gives it a nicer edge to my ears.
Lazing on a Sunday Afternoon vs Good Old-Fashioned Lover Boy: Comparable in terms of key and vaudeville influences. I prefer Lover Boy because of the guitar solo dynamics and the way harmonies are much richer when they're sung by the three of them (plus Mike guesting somewhere in the middle of the song) than when they're just Fred multi-tracking himself.
Seaside Rendezvous vs Good Old-Fashioned Lover Boy: Tie. To each its own - the one's got an impressive vocal work, the other's got some great guitars all throughout. I really couldn't pick one.
So, to sum up, I love both albums, but I love ANatO more.
John hated HS. Fred's fave singer was not PR. Roger didn't compose 'Innuendo.' Witness testimonies are often inaccurate. Scotland's not in England. 'Bo Rhap' hasn't got 180 voices.