This was actually a lot more difficult than I thought it would be. In the end, I had to go with HTDAAB. Based purely on musical quality.
You can't deny it that U2 have learned how to better use their music to support their message over the years. I'll take A Day Without Me and One Step Closer for instance. Both songs deal with the idea of mortality, but you wouldn't think so, based upon the musical style of A Day Without Me. ADWM is kind of cool in the sense that it doesn't sound as you'd expect it to, but it doesn't really invoke as much emotion as it should (for me, in any case.) While I love the song, it sounds too "happy" for me to feel anything. So I think U2 have really matured in that department - using the music to reflect the idea.
Next, the flow. Boy flows really well...because a lot of the songs sound similar. Almost all of the Boy songs follow the format of slightly distorted guitar plus delay, fast bass lines, and loud drums. The only exceptions to that are An Cat Dubh/Into The Heart (EDIT: forgot The Ocean) and Shadows And Tall Trees. HTDAAB, on the other hand, has bad flow...but at least there's a discernable difference between the style of most of the songs. Vertigo is very different to Love And Peace Or Else, which is very different to A Man And A Woman, which is very different to One Step Closer, etc. It's a little more interesting, that way, so HTDAAB gets the upper-hand in that respect.
Finally, I looked at the number of good songs on each album. This is how it panned out for me:
Boy: I Will Follow, Twilight, Out Of Control, A Day Without Me, The Electric Co.
HTDAAB: Vertigo, Miracle Drug, Love And Peace Or Else, City Of Blinding Lights, Crumbs From Your Table, Original Of The Species, Fast Cars.
HTDAAB has more, so it's ranked a little higher. I wanted to look at lyrics as well, but... I think Bono's lyrics suck on Boy and I think they suck on HTDAAB. Not much to say, really.
I really do think this sort of poll is far more interesting than 90s era U2 versus 00s era U2.
When it comes to 90s U2, I just automatically vote for whichever album HTDAAB/ATYCLB is being pitted against in the poll, because there really is no question for me as to which era is better. Musically and lyrically, I think U2 were on a planet of their own in the 90s. But this kind of poll actually requires some thought!