Potting sheds

If you can't do both go for the greenhouse. It's more flexible. A greenhouse can double up as a potting shed in spring, whereas a potting shed can not double up as a greenhouse. I would also strongly recommend that you get at least one protected 2.5mm cable to whichever you choose. Again, it's all a question of flexibility.

I see you have got a teenage offspring, perhaps you could get him to convert part of your shed into a greenhouse, taking out the window and part of the side, that is if you have space for it in front.

I agree with Muddywellies - a greenhouse is a money saver as well as a great place to be in bad weather - pottering! You could use part of under the shelves to store pots and trays if you haven't got anywhere else. I also agree that electricity in there, if you can afford to have it done, makes a huge difference in what you can grow. I have an electric fan heater that keeps mine frost-free, and also a heated propagator I was given. What a difference in getting seeds to germinate!

I'm another one who uses the undershelf area of a greenhouse to store pots/tools in. It can look untidy on the outside but one trick I use is to grow plants just outside that come up to the level of the shelves but not above them (so you don't cut down on the light too much).

Just got rid of our potting shed, ended up as a storage area, agree with comments a greenhouse with a heater, especially for winters like this one.

Plants need the light of a greenhouse, but tools don't care! So go for the greenhouse every time. And just think, you won't have to keep trekking from the potting shed to the greenhouse with trays of plants!