I just recently switched to a new hard drive on my PS4. Initially, I became paralyzed with sheer horror at the thought of having to redownload ESO (game + all updates). The first time around, that process took about 9 hours. However, I learned a little trick since then that drastically improved my download speed this second time: Rest Mode. Unfortunately, I only discovered Rest Mode near the end of the 9-hour first-time-downloading-ESO experience, so it didn't do me much good then, but it worked wonders this time around. Admittedly, the new, larger hard drive likely contributed to a degree; still, the download would have taken much longer had I not put my PS4 in Rest Mode. I'd say it took 3 hours, tops--a vast improvement from 9.
If you haven't already, make sure to close all other applications and definitely put your console in Rest Mode. Don't bother too much with the DNS server tricks; I tried those at first and didn't notice any remarkable improvements in download speed. Rest Mode + watching a few hours of television programs, and it'll all be over soon enough. Eventually. Probably best to also remove/cover your clocks; it can get depressing being constantly reminded of how ridiculously long the download is taking.
Eh, I wouldn't put all my faith in rest mode. The PS4s primary objective isn't to update right away in rest mode. It's to conserve power. The PS4 isn't always connected to the internet in sleep mode either, only until it's timed interval of packets that it sends and recieves kicks in and then it starts downloading an update.
So essentially, it could start downloading hours after a patch is released or it could be within minutes.
Several times I've had rest mode on throughout the night and it only started downloading updates when I turned it back on, including today when the patch was released. And yes, the option to update while in rest mode is indeed turned on. And I turned my PS4 on roughly five or six hours after the patch was offically released.
PSN is a cluster at times. Its speed cap bottlenecks my 250 megabit internet speed to about 40. Resulting instead of roughly 25-30 megabytes a second, to a measly 3 - 5 megabytes per second. 5 megabytes a second is the fastest I've seen my PS4 download.
OP, the only thing I can think of, is that a majority of the users are downloading the patch alongside you now, and when a data cap is already in place, it bottlenecks the speeds even more when hundreds if not tens of thousands of players are doing the same as you.(Think of the PVP queue in ESO, same thing)
You could also change the default PS4 DNS settings to a different one. I find it works much better in terms of speed and buffering on the Netflix, Youtube apps and yes even download speeds.(This wouldn't help your "preparing to download" issue, but possibly the download itself.)
126.96.36.199 is Googles DNS setting (The one I'm using). Hope that helps!
As to the guy above me, you should find a DNS closest to you. Googles DNS is in Mountain View California, so roughly 20 miles from my house. The default DNS the PS4 has is located in Texas. It's really common sense here on why I see improvement.
There are several free DNS locations at your disposal. Pick one that is highly rated and is closest to you.
As well, in terms of not seeing performance from changing DNS locations, also reflects on the PSN server itself. *Note* Using Netflix, Youtube and other PS4 apps don't require PSN to use, try testing these out too with the DNS change.
And to your new hard drive theory, your harddrive doesn't really have an effect on download speeds. Especially when you're not even downloading at around the gigabit speed.
Theoretically if you were, you could download ESO in minutes and in that case, the default hd in the PS4 can surely handle that. So saying the default hard drive will cripple an obvious speed cap on PSNs part that significantly less than the HD can handle, is obviously false.
I honestly can't understand all this speculative DNS changing. DNS resolutions are generally cached based on a record's TTL unless the PS4 downloader performs constant queries it really shouldn't affect download speed at all. The only thing I can think of that this could be doing is tricking whatever load balancer the PS4 is using to swap to another one, I'd imagine the content server uses your IP to geolocate and not the resolving server.
But I digress... same issue: come home.. almost everyday I turn my PS4 on I get an update for a game I've not been playing.. but for every occurrence of an ESO update it only starts when I turn it on.... pretty frustrating. I mean I'm not complaining as much about speed as here in Aus with our terrible internet(excepting the few lucky enough to get FTTP pre-coalition) I'm not excepting lightspeed.. but at 10Mb/s it should download fairly decently.