So I'm finally getting around to answering this question.
Was ToD originally a remake of the first game? Let's see…
[Pre-Release]
First things first, let's look at the GDC 2006 trailer. This one doesn't have a lot of material to work with actually, but it's enough to get by.
So, does this screenshot look familiar to you?
On first glance it just looks like something from Metropolis that didn't make it into the final game, but it is actually a next gen version of the first shot in R&C1 Metropolis:
The main thing to keep in mind here is that it never made it into ToD, coincidence? Probably, but I'm not one to believe in words like that.
After that there's not much to talk about, until the end that is…
This one is a bit of a stretch, but look at that logo, it's much different than the final one and it looks very, very close to the first logo. Was it a placeholder? Maybe, but it's woorth noting that ToD is the only game in the series to have a placeholder title so far, or at least one that was unveiled to the public.
Now there's nothing much to talk about with the exception that these trailers are really pushing this thing about Ratchet past. People who have played the game before will probably call me crazy for mentioning this, but trust me and bookmark this point for later.
There's also this screenshot where Ratchet is holding a weapon/gadget that looks really similar to the old Swingshot and due to these games' tendecy to mix grinding with Swingshot targets, I'd say it's not a bad guess.
[Post-Release]
Now, onto the good stuff.
I'll start with the story since that's where the most similarities lie and then I'll move on to graphics and gameplay mechanics.
Now, similarities between the two stories are all over the place, so let's begin:
At one point, Ratchet has to fix/build his ship on Fastoon, a planet that is very similar to Veldin when you boil it down;
Ratchet acts like a jerk to Clank for no reason during the second act;
Qwark is working with a person in power who happens to be really short;
Tachyon (the person in power)'s goal is to find a new home for his species;
Ratchet and Clank are wanted criminals.
At one point Clank is holding onto a ledge so he and Ratchet don't fall into the pit of death;
Both Drek and Tachyon fight Ratchet in a giant mech.
All right, that covers all of the story similarities (at least everything I could gather, feel free to add anything to the list), let's talk about Ratchet's past.
The game has NOTHING to do with Ratchet's past, it's mostly about the lombaxes and Ratchet's father, so is it possible that, when referring to Ratchet's past in the trailers they were hinting at the fact that this game was a remake… eh, a big stretch but I'm willing to believe it.
Now, onto graphics and gameplay mechanics.
As I said above, Veldin (at least R&C3 Veldin) looks almost identical to Fastoon, a level in which you fix Ratchet's ship just like in the first game.
Fastoon is also the final level of ToD, much like a certain other planet I'm certain I don't need to mention.
Other levels that are pretty much identical to each other are:
Mukow - Batalia
Rykan V - Gaspar
Jasindu - Novalis (yes, Novalis)
Reepor - Orxon (despite lacking the green fog, Reepor is similar enough to R&C1 Orxon)
There's also other similarities besides the planets:
Ratchet's outfit looks like an upgraded version of his old school vest (green pants, no helmet, orange vest, green symbol on said vest…
Ratchet uses the Omniwrench 8000 in this game, which doesn't happen in any of the other Future games.
ToD is the first game since R&C1 to have a proper flamethrower.
The Drophyds bear an uncanny resemblence to the Blaarg, despite having pupils…
The GrummelNet dudes look like that one Gadetron guy in the vendors.
That's all I could gather up and be bothered to share with you guys. The thread is not as in-depth as I hoped it would be and it's probably full of gramatical errors, but eh, discuss.
