Shell is the most simple to calculate so lets start with them. I tried to calculate how many litres of diesel I had to use to get 100 airmiles. I used the Petrolprices.com website for my postcode.

Shell Driver’s Club

Price here is irrelevant though as they give you 1 airmile for 20 litres. The website does not specify for which kind of fuels so I presume it is irrelevant. That makes:

2000 litres of diesel for 100 airmiles

Tesco Clubcard

Its more complicated here. You get one clubcard point for every £2 spent. A litre of diesel is about £1.35 (as of March 2011). Usually I will fill up my tank which is 60 litres -> about £80 which gives 40 clubcard points. 100 points give you 1 voucher pound so mathematically that would be 0.4 voucher points for 60 litres. That is 0.00667 voucher points per litre of diesel or 150 litres of diesel/1 voucher point.

Now, Airmiles give you 50 airmiles for 2.50 voucher points, so that is 5 voucher points for 100 airmiles. As 150 litres come to 1 voucher point, 5 voucher points (for 100 airmiles) come to 750 litres of diesel.

OK. This calculation is a bit complicated so I made an equation to make it easier and more accurate. The value is actually 740.

So about 740 litres of diesel for 100 airmiles.
Before the price change at Tesco and Airmiles this was 400 L/100 airmiles

Conclusion

That makes Tesco’s savings scheme 2.7 times more economical. you should know that this used to be much better until late 2010 as it was 5x more economical. However Tesco made a much worse offer on exchange of fuel for Clubcard points and also Airmiles gives you only 50 airmiles for the same number of voucher points, when before it would give you 60. So together they are now giving you almost half the value they gave before.

I do understand that some numbers are rounded and the calculation is not linear but it does show the huge difference in the schemes for airmiles. Also you get more airmiles with diesel and/or higher prices with Tesco than you do with Shell. If the prices would go down you would relatively do better with a scheme per litre of fuel than per pence spent, but the absolute difference is still very much in favour of Tesco Clubcard. Not to mention that you get more points with Tesco as you get them by buying anything at the shop, not just the fuel.

And y the way, I am not affiliated with any company mentioned here but I have used all. If my calculations are incorrect please inform me through my contact form.

The Math

To make it easier I have made an equation for this:

L/100 airmiles = 10,000 x A x B / C

Where:
A = voucher points per number of airmiles (example 2.5/50)
B = how many £ per 1 point spent (example 2)
C = diesel price per 1 L (example 1.35)

To get the factor F of how much the Tesco scheme is better than the Shell scheme you can use the following equation:

Where:
A = voucher points per number of airmiles (example 2.5/50)
B = how many £ per 1 point spent (example 2)
C = diesel price per 1 L (example 1.35)
D= Shell fuel L per 1 airmile (example 20)

As of March 2010 that factor is 2.7. So Tesco is 2.7 times better than the Shell scheme.