Personally, I think one of the biggest advantages is simply not needing to worry about local infrastructure as much. While cloud may not necessarily mean cheaper, it certainly means more consistent, and not nearly as much CapEx (the costs go back towards your OpEx).
The ability to ramp up additional infrastructure without spending nearly as much time developing sizing requirements, ordering hardware, racking, cabling, configuring, and then ultimately maintaining the systems can be tremendous. Even more so when you might have a bursty business where a large percentage comes during one or two periods of the year, but you need to maintain peak infrastructure during the whole year.
With a cloud deployment, you can spin up resources as you need them, and then tear them back down during quieter periods. It's this elastic scale that is the real driving factor around business.
If your customer service goals stem around access to services, or your website, or your support staff, then making sure you pick a system that has this on-demand, elastic scale is critical. If you're looking at hosted phone systems, make sure you have them demo to you the ability to scale from 10 phones to 100 phones in under 2 hours. If that is not possible, then you need to keep looking (and they aren't cloud; they are simply a hosted PBX).