Sorry, but I don't get why fuel and other overheads can be disregarded.
In the example both traders use £10 of petrol to get to the Customer. Non-vat has to pay £10 for his fuel, VAT gets 20% back so in effect only pays £8 (although may not see that until 3 months down the line)
That seems to go some way to redressing the balance.
I haven't disgregarded it, but it acts the same way as any costs - I gave the example and started off with £100. Go back to my example, and re-do the maths and you'll see what I mean. If I take your £10 gross fuel costs as an example (that's £10/1.2 = £8.33 Ex VAT). NewBoy and LoadsaMoney both have net costs of £108.33 and gross costs of £130 now. Mrs Jones can still only pay £170, so NewBoy makes a profit of £40 (instead of the £50 before).
So Newboys total profit is £40, whilst LoadsaMoney makes a profit of £40/1.2 = £33.33, and pays £6.66 to the VAT Man). I have just used my quick way, rather than the detailed way, but if you work through the details you'll see it is the same.
When you say goes some way to redress the balance - it is only because the profit has been reduced from £50 to £40 on the job - so LoadsaMoney only now has to pay the £6.66 instead of the £8.33 to the VAT man. If both firms can still retain their £50 target profit, and encourage Mrs Jones to pay £180 (instead of £170) there is no difference to my original example.
Essentially, NewBoy will always be better off whenever both firms make money - if both make NO profit in the year, then there is no difference, and if each firm makes a loss, it is of course better off to be VAT registered, and my last para of my initial post still stands :
Last para : "So if your firm makes a profit in the year you'll lose out."
The more profit you make, up until the VAT threshold, when you need to register for VAT, the better it is to NOT be VAT registered!