Short answer - If you don't know reasons yourself, you probably don't need to switch - just stick with whatever you use.
Route53 may be more reliable, may be faster, have some features that help integrate it with other AWS services, but you don't need any of it. If you care about the difference between 99.9 and 99.7, or if you care about 100ms vs 150ms, maybe it makes sense to start compare DNS services.
Btw, GoDaddy also offers premium DNS, paid monthly. And also there are many various DNS providers with prices ranging from free to hundreds dollars monthly.
Some of things to consider when choosing DNS provider: real uptime, uptime SLA, responce time (around the world - wherether your visitors reside, and around the clock), limits - like amount of queries or number of records or minimum TTL, price, features like DNSSEC, IPv6, dynamic DNS, account security fetures, supported record types, geo-DNS or load-balancing/failover, API etc.etc. - just look at specs of various DNS providers and you will see what features may be different.
Again, it's all small details. When you drive for a rally or operate twitter.com you double-check every detail. But if you just drive to your office and back, you aren't ought to know whether your engine is direct-injection or carburetor.