Probably a lot less than it costs to build, ship, and actively power the displays.
It's easy to estimate: if the displays + lifetime power costs more than all the posters, then chances are they use a lot more power. The cost of electricity isn't one of those externalities a business can hoist on society - it has to pay for each kilowatt-hour and that cost is easily quantifiable.
But why would TfL replace their old school displays with LED displays if the latter cost more than the former in the first place?
If they are gaining some sort of monetary incentive from replacing poster displays with LED screens, and your reasoning holds true, then perhaps in the greater scheme of things the LED displays do use less 'power'.
It's easy to estimate: if the displays + lifetime power costs more than all the posters, then chances are they use a lot more power. The cost of electricity isn't one of those externalities a business can hoist on society - it has to pay for each kilowatt-hour and that cost is easily quantifiable.