It depends. (Of course.) The short answer is: Not only don't we know, we can't know. The long answer uses the word "however" a lot.
Shared hosting has a well-earned reputation for volatility. You're sharing resources with other people. Who knows what they or the visitors to their sites are about to do? However, the most common causes of downtime are specific to the affected site. An expired domain, runaway scripts, or running out of funds are much more likely to cause downtime than a service failure.
We find that when people ask about uptime, they expect a magic number with a certain quantity of nines in it. That number allegedly represents the fraction of the time our service is available. However, the availability of "the service" depends on the definition of "the service." We host a large number of sites and they don't all move in lock-step. One person's downtime might not affect anyone else.
It would be easy (and blatantly dishonest) to pick an arbitrary definition that would allow us to claim 100% uptime, or any number of nines we want. Likewise, with enough hardware, something is always offline for maintenance. So we could make an argument for 0% uptime. (Though we prefer not to.) In the rare case where a production server crashes, it usually affects a small percentage of our members' sites for a few minutes. Sites move back and forth, servers go up and down, and most of it happens without any visible effect.
There's also the philosophical angle. If a server reboots in the forest, but no one tries to access it, was it really down?
At many providers, your site is 100% dependent on the availability of a single physical server. If it fails, you're out of luck. Our clustered approach provides resiliency against many types of hardware problems. However, we do develop and maintain our own clustering software. Occasionally something incredibly weird may happen here that would (or could) never happen anywhere else. Such events are rare, but not without precedent.
Sites hosted at NearlyFreeSpeech.NET run a small risk of being "collateral damage" of a denial-of-service attack not aimed at them. But the flip side is that we have extensive experience with such attacks. We're able to mitigate most small and moderate attacks without disruption. So although the risk might be higher, the expected impact is lower. There is (most likely) not much practical difference in DDOS risk between competent hosting providers.
All in all, our overall service availability is probably above average to very good when compared to other shared hosting providers. However, "overall service availability" is meaningless if your stuff is down. We understand that. One site offline because of a service malfunction is one too many. That's why we monitor our systems and services continuously from multiple offsite locations and respond to problems as quickly as possible, 24x365.