Pros:
WGGS - good academically, considering only 25% get in on exam and 10% on music;no bullying - largely dueto firm policies on bullying and strict but fair head; excellent teaching; excellent at non-acaemic subjects eg superb art, music, sport etc; less pressurised as range of academic abilities with the emphasis on everyone achieving their potential; large grounds; bigger numbers (180 per year instead of 90) so better facilities; sibling policy so if younger siblings (girls or boys) you only have to go through exam once; local catchment school so all pupils can travel by (good) public transport on relatively easy, short, cheap journey and will have local friends to travel with, hang out with etc.
HBS - better results academically and better university desinations for 6th formers (but that reflects that 100% of girls get in on exam so brighter to start with); more attractive building (but smaller grounds and no sporting facilities on site to speak of); v cut off location so fewer distractions (but makes getting to school harder!).
I went to HBS (and was happy there) but chose WGGS for my dd - from the relative length of my lists you can see why. I have been v happy with WGGS and would recommend it. If you live locally to WGGS you'd be mad to put your dd through a v lengthy and tiring commute to get to HBS - don't undersetimate how cut off it is and difficult to reach - 20 mins+ walk or bus from the nearest tube station and you have to get there first! No local friends, and if you have younger siblings you have to go through the whole entrance exam hassle again! (you now get entry at boys and girls grammar since cross-sibling entry was reintroduced for any younger siblings).
Also, apocryphally only, I believe WGGS is more nurturing than HBS as I have heard of bullying at the latter (know family of one girl who left as a result). Whereas all the girls I've met from WGGS have been lovely! Also, HBS is good for science subjects but almost no-one does arts subjects there these days. (13 doing A Level History v 90 doing Maths!)
Before deciding, I'd drive to HBS, pref at rush hour to get a realistic idea of the length of commute even if driving (obviously longer if public transport is used), or failing that at least check out the travel using the TFL site and/or google maps.
Both great schools - there probably isn't a 'wrong' decision here but there is a 'more right' one though.