In some or even many cases neither need necessarily apply.

It doesn't always have to be a populated valley that gets dammed. There's a decent selection of disused quarries, maybe some of the Highland lochs that have potential to create something like Dinorwig at minimal disruption to environment once complete. What I don't know is how those constructions compare in today's money to alternatives. Still, £70bn brings an awful lot of choices, especially when lifespan is indefinite, just periodic turbine replacements.

If the geography isn't available there's the Netherlands project that's pumped storage on entirely flat land. Involves building an artificial lake, with a cavern and turbines below it. Suitable rock for the cavern is quite a long way down, which adds to the cost, but also adds to the head so it should end up with significant capacity. As far as I know it is the first such scheme, so costs are projection only at this stage, but it looks pretty interesting if it turns out to be viable economically: https://o-pac.nl

Or the UK company that has a plan involving winching weights (thousands of tonnes) up and down disused mine shafts. The open question of course is how many of the world's thousands of disused mine shafts are going to be viable. If viable the advantage seems to be very low surface profile.

All these large-scale energy storage projects are in their infancy. I haven't heard of anyone breaking ground on a project multi-GWh capacilty. Until that happens, it's all hypothetical.

Also, I am no expert on the subject, but digging out underground reservoir sounds expensive.

Dinorwig is 10GWh. There were two backup sites chosen in the same immediate area to cover the case the main site had proved impractical. Many years have passed so it's unlikely they're still there, but geography is not lacking if the political will were there.

There is still bad feeling in wales about some of the valleys that where flooded in the 60's.

With devolved government now in Wales and Scotland and new Pumped storage will face more push back

Given rule changes even without devolved government repeats of the Liverpool reservoir would be much harder. Dinorwig used already existing disused quarries - not flooding a pristine valley.

In the case of Scotland it's been the Scottish government looking at using lochs. No idea what the case is in Wales.

Your version of head assumes discharge into bedrock. Are they building a cavern of many cubic hectares down there too?

That seems to be the plan - enough capacity to store the whole topside lake, which seems to be planned at 500m x 500m (depth 10m). No idea how feasible or economic it will be compared to caverns from hollowing out a mountainside.