I have my entire website behind a CloudFront distribution, and I used to have a Route53 zone, where the zone apex record for my website pointed to an ALIAS record for the CloudFront distribution.
However, now I'm switching to NS1 as a DNS provider. They also have a similar ALIAS record, however, there documentation states:
Geotargeting information is lost. Since it is the authoritative server for example.com that is issuing the queries for lb.example.net, then any intelligent routing functionality on the lb.example.net record will act upon the location of the authoritative server, not on your location. The EDNS0 edns-client-subnet option does not apply here. This means that you may be potentially mis-routed: for example, if you are in New York, and the authoritative server for example.com is in California, then lb.example.com will believe you to be in California and will return an answer that is distinctly sub-optimal for you in New York.
Basically, if I understand correctly, visitors of my website might be directed to a less than optimal CloudFront edge node.
Is this something I really need to worry about? For example: how big is the chance that a European visitor is directed to a CloudFront edge location in Asia?
You're correct, this change could result in visitors being directed to more distant CDN nodes than is ideal. This could result in lower performance for your website visitors.
Why are you switching DNS providers? Route 53 is fast, reliable, relatively cheap and integrates very well with AWS resources. It's 50c/month per zone then $0.40 - $0.70 per million DNS requests. It would take an exceptionally high volume website for that to become significant.
Update 1 By switching DNS providers you may shave a few ms off the DNS lookup time, but at the expense of sending your users to the wrong CDN node. This will slow your website down much more than DNS lookup being slightly slower.
I just tested DNS looking times for the NS1 and Amazon AWS websites, as I figured they use their own DNS servers. I tested from two locations - so a very small sample size, all within the US, but you could test yourself. Here's the timings.
So all in all you're making things more complex and slower to save about $0.75 per month. Suggest you stick with Route 53.