For licensed software:

Licensed software can be run on your server. You can download it or buy the software and then upload it on your server. Then once purchased you can do anything that you want with it. You can get the benefit of hosting it the way you want and even customize it according to your requirement. The initial cost is definitely going to be high and the debugging definitely claims a threat. The fees are going to decrease though and it will come cheaper. Though there are bugging elements there but you can find solutions for yourself or fully licensed solutions.

For Hosted Solutions:

The biggest benefit of hosted solutions is that the initial cost is very negligible, most of the solutions come with wizards and templates and you can also get lucky by getting the advantage of upgrading. Your host will take care of all the technicalities that the potential business owner or you might not understand or interest you. Thus leaving you all the time to manage your business and running your site more fruitfully. This is a good option if you want to stay away from all the IT issues or want to save by not having to hire an IT team for dealing with it.

So now ultimately it is your choice and personal expertise and contacts that it depends on which option you would want to go with.