I would personally choose WHMCS for two reasons. Firstly, it's familiar with both web hosts and their clients, this helps. Secondly, there's a huge number of useful plugins available for it. It really is the industry standard nowadays.
If you have to use either one of them go with WHMCS, Hostbill is overpriced, the support is next to nothing and if you need them you have to pay for a ticket. but if you use WHMCS keep it secure as much as possible with Mod_Security / Imunify360 so you don't have to stay up all night incase there's a patch. But yeah WHMCS over Hostbill.
I would suggest go with WHMCS. You will get lots of option to manage various things related to billing as well as other things too. It is easy to install and manage. We use it from too many years without any hassle.
The automate billing reduces your time. It is very user friendly and secure way of billing.
I don't have any idea about hostbill as I never tried it. I have been using WHMCS for 3 years and I am very happy with it. Simple and nice interface. The support is also great. Always get replied relatively fast. The template is also easy to customize so it can fit your current template. They have some addons but a bit pricey in my opinion. So far no negative review from my sel
I would suggest WHMCS we have been using it for years and never had a problem that was related to the software. We have had some issues however it was only from server settings needing to be tuned EX: PHP Limits. All has been working great for a long time now. I would give WHMCS a try.
Another reason is that they have a market place that users can create plugins for a number of things and it is very nice to be able to add to WHMCS to make it more suited for your company or needs.