To start with, I didn’t actually move as such because I already had most of my domains with Dynadot but I still had a few domains on GoDaddy.
In the past, I always found the DNS changes to GoDaddy domains extremely slow amongst several other things. Meaning, if you change the nameservers on a GoDaddy domain, it could take hours before the new nameservers fully propagate.
In the contrary, I found Dynadot to be extremely fast. When you change the nameservers, it takes a few minutes and you can see the new site. Dynadot also has an IP Lookup and Snapshot tool so that you can see the nameservers and IPs on the domain and also see an uncached version of your site to see if it has propagated. So even if your ISP hasn’t refreshed it’s DNS cache or your computer may still have DNS cache stuck, this tool allows you to see the current, uncached version of your site.
Here is their IP Lookup and Snapshot tool:
So recently I moved a server from HostGator to Amazon AWS with dozens of accounts on it. Most of the accounts had the domains registered on Dynadot and they went fast but when it came to changing the nameservers on the GoDaddy domains, issues arose and they took ver long to propagate. So I transferred the domain to Dynadot, did the server migration and then changed the nameservers and it was almost instant.
I recommend using Dynadot for domain registrations, renewals and transfers.