These figures have really suprised me, so to take the points make and to cut the figures a slightly different way, ignoring if it is renting/buying and assuming housing costs are equal in each scenario, at the appropriate LHA cap (effectively it is your "choice" if you live somewhere more expensive than the LHA cap), ignoring communting costs etc. (I've used my LHA cap for the purposes of the calculation)
Scenario 1 - One parent on £44k, other parent not working ATM - 3 children - ChB no longer payable due to HRT payer
salary 44k
less tax/NI £12k
give net/month = £2667
Scenario 2 - one parent works 16hrs/wk on just over min wage, other parent not working - 3 children
16hrs/wk at just over min wage = £5k
(no tax/NI due)
net/month = £417
- ChB for 3 Children (204/month) = £621
- tax credits (£939/month according to entitled to) =£1560
- HB/CTB of £775 (according to entitled to)= £2335 net/month
Scenario 3 one parent works FT on £15k pa, other not working ATM, 3 kids
salary £15k
less tax/NI = £12435pa = £1036/mth
- ChB for 3 Children (£204/month) = £1240
- tax credits £726/month (according to entitled to) = 1966
- HB/CTB of £488 (according to entitled to)= £2454 net/mth
So for a 300% increase in the FT GROSS income (15k to 44k) there is only a 9% increase in NET income. 
I've seen loads of posts saying "but higher rate tax payers can afford it", "if my DH was a HRT payer we'd be rich", "I wouldn't be whinging if DH earned 3 times what he does now"... etc. and TBH I was expecting there to be a much greater difference. Actually there isn't...
(As I've said before DH is not a HRT payer, so I've no personal axe to grind here)