Yeah, but it needs to be developer supported. For a game like Killzone you could play the 1st campaign level while the 2nd is downloading/installing in the background.

I recently swapped the PS4 500 gb HDD for a 2TB one, and the first thing I did was re-install all the games. Even the largest games like TLOU which takes 50gb only took less than 60 seconds and I removed the disc. UNless it only part installed it and even though I removed the disc it would continue to install the next time I put the disc back in? (I guess it might be doing that, no way to tell or see it though)

Exaggerating is also a profession (like they say here), but you're definitely onto something. The install times for some games are pretty ridiculous.

Here's a list of install times of some games:

Assassin's Creed IV:
Xbox One (offline, no update): 5 minutes 50 seconds
Xbox One (with update, fastest connection): 7 minutes 2 seconds
Xbox One (with update, 10Mbps connection): 10 minutes 32 seconds
PS4: 42 seconds

Need For Speed Rivals:
XBO: 09:25 (including update)
PS4: 00:32

Just Dance 2014:
XBO: 08:48 (including update)
PS4: 00:45

NBA Live 14:
XBO: 16:26 (including update)
PS4: 00:35

FIFA 14:
XBO: 16:06 (including update)
PS4: 00:34

Madden 25:
XBO: 9:38 (including update)
PS4: 00:38

http://kotaku.com/installing-xbox-one-games-takes-way-too-long-1471191836

PS4 secondary ARM chip installs in the background while you begin playing.

PS4 also has a hardware zlib decoder which rapidly decompresses data from physical media.

All these factors combine to allow you to begin playing very quickly and also install games very quickly.

Probably. I don't have any next gen console, but I can tell you that there doesn't exist a HDD that could transfer data at such high rates.

The fastest HDD has a write speed of about 250 MB/s under ideal circumstances. the fastest SSD about 500 MB/s under ideal circumstances.

on the HDD TLOU would need 205 seconds
on the SSD TLOU would need 102 seconds

Chances are that your 2TB HDD doesn't have 10000rpm and doesn't run under ideal circumstances and has a write speed of closer to ~150 MB/s, which would then take 341 seconds.

Cool, I didnt know that!

Doesnt the XBox One have that? and does that mean it will always take as a long as it does to install games?

Some of that is a bit more technical than my know how :P

All I do know is that the HDD I took out was 5400 RPM and the one I have put in is 7400 RPM (I think) but I havent actually noticed any increase in speed in reality, though I guess it could be nominal and not noticable without a stopwatch. 

If it has it, it's not listed in it's specs.  So we'll have to wait for someone who's really been paying attention to the XB1 to comment.

If you're referring to the background installation feature, both the PS4 and XB1 utilize it.  But, it appears that the ARM processor in the PS4 assists in the installation times...but yeah, would need more insight from someone who knows the XB1's internals better.

But even 341 seconds is much much faster than 1 hour the OP claims it takes XOne to do it.