I can't really vote as there's much more that needs to be factored in. It's always good to shop around, even if you're happy with your current provider, but if another provider offers things you want/need that you're existing provider does not it doesn't hurt to try
My suggestion is to retain your current provider and duplicate your setup with the one you're trying out, point your DNS to the new server, and if needed it will be easy to switch things back to your current host. Then "try out" the new host for 1-2 months.
While you'll be paying for 2 hosts, IMO the extra cost is worth saving the hassle of downtime during propagation & in the event you need to switch back.
For me big factor to consider when comparing and considering switching hosts is the difference in hardware, which not all people consider. Although costs could be considerably lower, we choose to stay with a provider with a very strong "premium" bandwidth network, and who offers server rather than desktop components.
You get what you pay for