A vented cylinder is fed by a cold tank in the loft and works on gravity, so its pressure is whatever the height difference gives you, which is usually modest. It is simple, tolerant and cheap to maintain.
An unvented cylinder is fed straight off the mains, so every outlet in the house runs at mains pressure, which is why showers from an unvented feel like showers. The trade is that it is a sealed pressure vessel, and that brings requirements: an expansion vessel, a temperature and pressure relief valve, and a tundish and discharge pipe that can take boiling water safely to outside without scalding anybody or running uphill. In a flat or a basement, finding that discharge route is frequently the hardest part of the whole installation.
Hot Water Cylinder is priced after the job has been seen, anywhere in the areas we cover. Send the postcode and a few lines about what it is doing when you contact us, and the answer comes back in writing.