Buying means you own the equipment outright and carry both its value and its depreciation. Leasing means you pay to use it for an agreed period while the lender keeps ownership. Buying ties up capital but leaves you with an asset; leasing preserves cash and spreads the cost, but you build up no ownership.
Buying outright avoids interest and finance charges, and the asset can later be sold or refinanced. The downsides are the up-front cash requirement and the risk that the equipment loses value faster than expected, or becomes obsolete while you still own it.
Leasing spreads the cost into predictable payments and can make it easier to update equipment at the end of a term. But the total paid over the term will normally be more than the cash price, you are committed for the full period, and ending early usually triggers a settlement figure. Condition, mileage or hours limits may also apply.
Hire purchase sits between the two: you spread the cost like a lease, but own the asset at the end like a purchase.
Which works out better depends on how long you will keep the asset, how quickly it depreciates, your cash position and your tax position. The accounting and tax treatment differs between the options, so involve your accountant. Terms available to you depend on lender assessment.