The short answer is ownership. With hire purchase you are buying the asset in instalments and it becomes yours at the end. With a finance lease you are renting it — the lender keeps legal ownership and you either continue renting, sell it on their behalf, or return it.
Hire purchase suits equipment you want to keep long term: vehicles you’ll run for years, machinery central to the business. You take the depreciation risk, but you end up with an asset on the balance sheet.
Finance lease suits equipment you may want to replace, or where you’d rather not tie up capital in something that dates quickly. Payments can be lower, and rentals are usually treated as an operating cost — but you won’t own it.
Which works out better depends on your tax position and how long you’ll realistically keep the equipment. Worth a conversation with your accountant as well as with us.