Can performance matter between multiple domain registrars? What should one measure to determine which registrar is more performant? The shared hosting will be at a separate provider so I will use the name servers of the shared hosting.
A registrar is your "gateway" to a registry. For any kind of operations on a domain name, you need to go through it (most of the time, as it is a common setup for many TLDs, but not all: with some you still deal with the registry directly because there are no registrars, with others you can deal with registry directly or with registrars). Once it is done (domain created, nameservers updated, etc.) your registrar does not play a role into your domain name being in working state (this depends only on the DNS globally and your services' configuration and states), with the following caveats:
- of course if the registrar is also the DNS hosting provider or the web hosting provider or the email hosting provider or any other service besides pure domain name registration, then it still plays a role, so its performance impact your domain name
- your registrar still controls your domain in the sense that it can send commands to the registry; if, for example and for whatever unknown reasons it starts to be mute and not properly act on transfers, change of nameservers or even domain name renewals, then your domain is at risk of non working (various horrible cases happened in the past with bankrupt registrars or other kind of disputes, see the famous major RegisterFly case or more recently the AlpNames case)
- as a subcase of the previous one, note that for gTLDs, ICANN has specific rules about this, like amount of time the registrar may take between taking your command and sending it to the registry, processing transfers, etc. This does not apply for ccTLDs.
- there are some specific edge cases where a registrar still can have an impact, besides the obvious "nameserver changes" and "handling transfers", you also have things around DNSSEC: for normal operations you need to change your keys "regularly" at registry; right now this needs to go through the registrar (even if they are other technical solutions, no registry really use them for now), so if it does not do DNSSEC at all (still happens a lot) or is clueless about it or is not providing you with the adequate tools (proper UI and/or API) then your domain name performance may suffer in the sense that in case of DNSSEC problems or urgent change of keys, if the change does not happen your domain will stop to work (more precisely: resolution for names in your domain will stop working which makes all services offline basically).
However, another theoretical point can also exist (I have no hard data about it, but see no reason while it wouldn't exist): reputation. There are providers of domain name reputation that base their answer on the "freshness" of the domain, and Internet search engines are doing the same thing, all based on the assumption that a domain name created 10 years ago should be more "trusted" than a domain name created 10 minutes ago. In that sense this can impact the performance of the domain because emails sent "from" it could be tagged negatively, etc. And the theoretical point could be: such reputation lists could as well also take into account the registrar used for the domain name, as some registrars may be deemed less trusted than others or more or less compliant with rules and open to all kind of abused and how they handle them, or based on their country of jurisdiction, etc.
Of course, as @DominiqueH says, performance could also be judged through things like customer service (how much do they understand your request, how fast they are acting on them, etc.). You could take into account price too (good quality/price or not).
Related: various registries attempts sometimes to put a "quality index" on their registrars, to order them. Some cases:
- judging registrars by how good they are at handling DNS (even if not their own): when registries check technical configuration of nameservers, registrar submitting bad ones could be given a negative note (the .FR registry did this in the past)
- judging registrars by how fast/good they handle abuse reports and so, and denying them access to financial promotions/rebates by registry if not good enough (the .ORG registry is planning to do that: http://domainincite.com/24378-dodgy-registrars-could-be-banned-from-org-promotions)
I have never seen any technical performance variations between registrar. But there are a lot of variation in terms of customer service and ease of use. You usually never talk to a registrar unless something wrong is happening, when you need fast and efficient service. Select a well-known registrar, with a 24/7 support, including live chat (I find it much efficient than phone support most of the time).