I had this issue as well a while back at Heathrow. I'm a student and hence always look for the cheapest deal, however the rare times I find such a deal, its not for the dates I need the car for. I find SIXT to have a much more superior fleet and better service, however they refused to match a price which a week before the booking was the same price as the competition (Europcar) when I booked.

Come on Sixt, be a little more lenient in your pricing