How are Wham anything but a boy band? They were the first, pretty much, but they were definitely a boy band (and I was a big fan).
Take That's embarrassment of riches singles back catalogue far outweighs that of Backstreet Boys, I think. Backstreet Boys did have some great records - Backstreet's Back (number 2 in the UK, 1997), I Want It That Way (number 1 in the UK, 1999), and Larger Than Life (can't recall chart position off the top of my head, but top ten, 1999), for instance.
But Take That's amazing singles include:
It Only Takes a Minute (1992, UK chart position: 7)
Could It Be Magic? (1992, UK chart position: 3)
Pray (1993, UK chart position: 1)
Relight My Fire (1993, UK chart position: 1)
Everything Changes (1994, UK chart position: 1)
Love Ain't Here Anymore (1994, UK chart position: 3)
Sure (1994, UK chart position: 1)
Back for Good (1995, UK chart position: 1)
Never Forget (1995, UK chart position: 1)
Then, post 2006 comeback, we have:
Patience (2006, UK chart position: 1)
Shine (2007, UK chart position: 1)
Rule the World (2007, UK chart position: 2)
Greatest Day (2008, UK chart position: 1)
The Flood (2010, UK chart position: 2)
Love Love (2011, UK chart position: 15)
These Days (2014, UK chart position: 1)
I mean, these are personal highlights, but I could go on. Apart from anything else, Take That are the only band I can think of to stage a comeback ten years on from when they disbanded and still be just as good. So for that reason, and sheer quantity of top quality singles, I prefer them to Backstreet Boys.
Of course, if you're rating them on any other criteria (I accept that the primary audience for both was teenage girls) then I cannot comment. :)