How many races are on your ballot? Next Tuesday, I'll have 11 races to vote for, plus 4 ballot referendums. That's probably a median election ballot in the US.
In the UK? Typically just one race: you vote to elect your local MP.
You might also vote for someone to represent you in the devolved Welsh/Scottish/Northern Irish governments if you live in those countries, but that's only 15% of the population and those elections aren't necessarily on the same day as the general election.
In the UK you usually have 1-3, fewer since we left the EU.
However, the number of ballots is relatively immaterial for two reasons:
Spend: In the UK, price of counting ballots is far lower than price of paying poll booth staff. It costs approximately £0.10 per person (note, not per ballot) in the UK to count ballots in a nationwide election (as opposed to about £0.35 on keeping polling booths open). It’s likely that if the number of ballots went up by a factor of 10, further efficiencies would be found, but simple ‘ballots counted per hour’ metrics imply that the marginal cost should be relatively affordable.
Difficulty: While running a fair and free election is undeniably challenging, it naively would appear to be much less work than E.g. the USPS does each day to deliver the daily 300M pieces of mail.
While the USPS is a government department, it is allowed to charge its users and does so.
The people running elections don't charge voters for voting.
So I'm not sure it's useful to compare the two?
(That the Americans feel like they need government mail when the supposedly more socialist Europeans mostly managed to privatise their former monopolists probably tells us.. something?)
I would expect that the amount of time it takes to tally a paper election is related to how many people you have counting.