On the surface (like with a lot of things in payment), it would seem to make sense to use a HOP. But, unless you are a mom & pop merchant with little choice and a serious lack of technical resource, be aware of the compromises that you are making. It is tempting to "solve" your PCI requirements by letting someone else host the order page and therefore handle all the credit card storage. Here are a few things to think about;
1) whose data is it? If you ever decide to change providers or take the order page back under your control, will you be able to easily get your data back? Does your contract cover that? Is your provider prepared to do this in a timely, efficient, and secure manner?
2) maintenance windows? Remember, yours for the rest of your site and your providers for the HOP will rarely be the same so there are going to be times when your store is open, but your checkout page is not available.
3) security settings? If your consumer has their security settings set high, the transition from your shopping pages to the HOP may cause a warning box to pop up. This could lead to confusion, concern and of course the dreaded shopping cart abandonment syndrome.
4) branding/look & feel? Most HOPs allow you to attempt to make the page look like the rest of your site but it will never be perfect and therefore again this transition could lead to shopping cart abandonment.
5) customer service? If you are using a HOP, are you going to have the info you need to provide customer service? Are your CSRs going to have to switch from one system to the other to get access to info?
6) chargeback handling? Does the HOP give you adequate info to prevent and/or handle chargebacks when they arise?
I am sure there are things that I am missing but I hope I have at least caused the people who are in a position to make choices on matters like this have some add'l food for thought to help make an informed decision.