Yeah this is a super exciting development!
So let me explain some of the questions brought up here -
Why's it so big?
Two main reasons-
1) Methalox propellant. Liquid Methane is about as dense as liquid oxygen, which is to say not very dense. So to get the same amount of performance as an equivalent Kerosene rocket, you need much bigger tanks.
2) It's sized for RTLS (or possibly drone ship but more likely RTLS) landings for every mission in its payload class.
This second point is the main driver because if the answer was only 1), the rocket would be much smaller (see Delta IV which is smaller and uses even less-dense Hydrogen propellant). Blue Origin is a big proponent of re-use and especially RTLS landings which take ~30% extra propellant to pull off for a given payload size.
Now because of 1) and 2), you wind up with a very large rocket that launches payloads in the F9FT (not F9H) class. Based on the thrust numbers (which allows for a decent, but not perfect, first order approximation of payload size) and the above facts, this rocket will likely be capable of placing payloads into LEO/GTO that are in the upper range of the F9FT's capabilities, not the FH. The FH will be capable of a larger payload than the New Glenn 2 stage variant.
The New Glenn 3 stage variant will likely beat the FH in payload size to GTO or TLI/TMI/beyond-Earth trajectories. That is because the proposed 3rd stage of the New Glenn will be a Hyrdolox system based on their sub-orbital work on New Shephard (it will use a vacuum variant of NS's rocket engine). On the scale of specific impulse (rocket efficiency), Kerolox<Metholox<Hydrolox.
Now for first stages, the specific impulse is not as important as thrust. This is how the Falcon family manages to place such huge payloads into orbit despite the relative inefficiency of their engines. However, for upper stages, specific impulse dominates and the higher your specific impulse, the bigger your payloads can be. So the New Glenn 3 stage variant will likely beat FH for payload mass but likely not by as large of a margin as you would expect given the rockets size (remember 1) and 2) from above still applies to stage 1 and 2 of New Glenn).
Some other key info -
Blue Origin is building a factory to build New Glenn near the launch site in Florida. This allows them to make their rockets as big as they want. SpaceX makes their rockets in California and they decided that their shipping method to the launch site would be by truck. This limits how wide the stage can be, which is why Falcon ended up so tall and skinny. The rocket is about as long as it can get too or it will turn into a spaghetti noodle in flight.
On Mars-
There is currently no public plans for a 3rd stage for Falcon vehicles. The amount of mass that F9FT/FH can throw at Mars is based solely on what the rocket can currently do. The 3 stage New Glenn rocket will likely exceed this mass to Mars based on the efficiency of it's 3rd stage. There's a good chance that the 2 stage variant would exceed F9FT's throw-weight to Mars as well. But the 2 stage variant will likely not exceed FH's throw-weight to Mars.
Also, Blue Origin is not fixated on Mars the way SpaceX is, so their architecture is not developed toward that bent. Bezos wants to make humans a space-fairing species but is not wedded to the idea of starting a Mars colony. So don't look at his rockets and think 'oh man that can get so much mass to Mars', instead think, 'oh man that rocket can put so much infrastructure into LEO'.
On fairing size -
Falcon already flies one of the largest fairings on the market. There are not too many payloads that are too large for it and if you factor in the payloads that exist in fact and not just on a drawing board, then pretty much none exist that are too large for the fairing. Bigelow's modules are an example of one payload that would be too big but I would not count on them producing hardware. From everything I've read, Bigelow Aerospace is one of the worst-run of the 'new' space companies.
They once hired people who moved out to Las Vegas on their own dime and laid them off on their first day. It's a cluster over there. So while it's fun to speculate about their modules, they are vaporware until they exist. Having said that, Bigelow himself has deep pockets to continue bankrolling the company. Also, keep in mind that the 'agreement' between ULA and Bigelow is unfunded (Bigelow is not buying rockets yet, they're essentially just studying the problem together) and would require ULA to develop a 2-engine Centaur (2nd stage) variant of the Atlas V. So even though it would fit in their fairing (just barely), it would actually take a lot more engineering work to pull off in the form of a new 2nd stage rather than a re-design of a fairing.
Random stuff -
New Glenn has more thrust than F9FT but less than FH. Payloads will likely be something like-
F9FT =~ NG2S < FH < NG3S but that also depends on the specific orbits and whether or not F9FT/FH are doing ASDS or RTLS landings. Both variants of NG will likely RTLS.
Blue Origin has not mentioned 2nd/3rd stage re-usability. That's also a much harder task than 1st stage re-use and would warrant it's own post to talk about.
On naming scheme -
I agree that New Glenn doesn't have a nice ring to it. That said, I don't hate it and I do like the overall scheme. As to nationalism - uhhhh not so much. People read too much into that. Blue Origin and SpaceX both want to see humanity become space-fairing in different capacities. They do not want to make just America a space-fairing nation. If they want to name their rockets after American heroes or chant 'USA!' after a landing, who really freaking cares? They will both launch or already do launch international customers and will eventually fly international astronauts/colonists. The nationalism angle is such a dumb thing to get hung up on. And to restate an interaction that made me chuckle on reddit -
RedditGuy1 - When they start chanting 'USA' after a landing, it makes me feel excluded as a non-American.
RedditGuy2 - Oh I'm sorry, did you contribute?
Acronyms -
F9FT - Falcon 9 Full Thrust
FH - Falcon Heavy
TLI - Trans Lunar Injection
TMI - Trans Martian Injection
NG - New Glenn
NG2S - New Glenn 2 stage
NG3S - New Glenn 3 stage
BO - Blue Origin
SX - SpaceX
BA - Bigelow Aerospace
Isp - Specific impulse
ULA - United Launch Alliance
GTO - Geostationary Transfer Orbit
NS - New Shephard
That i find most amazing thought is that i already knew most of the technical aspects thanks to playing KSP...
