HP doesn't have a mileage limit and the final payment is typically very small. As a result you will find it no cheaper -infact its usually more expensive because traditionally the APR will be higher - than a bank loan. If you have found a product where the monthly payments are lower but there is a significant 'Optional Final Payment' then this is a PCP product (BMW call it 'Select').
Essentially, you rent the car from BMW -it isn't your car. At the end of the agreement you simply hand the car back and walk away with nothing to show for it, or alternatively you can purchase the vehicle by paying the Optional Final Payment, which you could also finance if you wanted. PCP agreements will have mileage limits because the deal is structured based on how much the car is worth to the lender at the end of the agreement, and the mileage directly affects this.
I'm going to be a bit controversial here but IMHO the entire point in a PCP is to enable people to buy cars they couldn't otherwise afford. IMHO it's not a sensible way to buy the car, you end up swapping short term higher expenses for a solution that, over the longer term, is more expensive.
With HP the lender again owns the car until you make the final payment, but there is no big payment at the end and the final payment is similar to your normal monthly payments. Once you've made the last payment you then own the car. But you may as well borrow from the bank unless you get a killer rate on a HP - then its your car and the monthly payments are no different. However, one thing HP offers you that a bank loan doesn't is the ability to borrow huge amounts of money with a crappy credit rating. As the lending is secured on the car its more secure for the lender than a bank loan therefore they are more inclined to offer credit to people who shouldn't be buying expen.. no err, people with lower credit ratings
If you want to borrow money to buy a car it is my opinion that the best way to do this is to get as much deposit as you can and use a bank loan to pay the rest. That way its your carf and you are not simply driving around in somebody elses car just so you can keep the monthly payments at a level you can afford. This is just my opinion and I'm sure I'll get flamed by a bunch of PCP holders who strongly disagree with me, but hey
Sometimes there are exceptions. Some dealers/manufacturers will offer 0% or a low APR on some of these products in order to shift cars which otherwise are not selling, or in order to get rid of a load of new stock safe in the knowledge it'll come back in 2 years as quality used stock they can then re-sell. But make sure you do a full analysis on the total ownership costs of any of these deals and don't forget - dealers will quote you FLAT RATE to make it seem good value. Ignore flat rate. APR is the only rate that matters and is typically about twice the flat rate.