What actually differs
With financing you own the asset from day one and the funder holds a lien until it is repaid. With a lease the lessor owns it and you hold a right to use it.
Financing usually needs a deposit; leases frequently do not, which is why the monthly figure is lower.
A capital or $1-buyout lease is ownership in all but name and behaves like financing. A true operating or fair-market-value lease is genuinely rental, and the difference between the two is the end-of-term option, not the marketing.
When leasing is genuinely the better answer
Assets that date fast — IT hardware, diagnostic equipment, anything where a five-year-old unit is a liability rather than an asset.
When cash is the binding constraint and the lowest possible monthly payment is what makes the business work.
When you genuinely want to hand it back. Paying for the option to return equipment is only worth it if you will use it.
When financing wins
Long-lived assets. A truck, a press or an excavator has years of use and real residual value after the term, and owning that is worth more than the payment difference.
Total cost. Over the life of a long-lived asset, financing is normally cheaper than a sequence of leases.
Equity. A paid-off asset is unencumbered collateral for the next facility, which a leased one never becomes.