I suppose the current popular contender for commercial/non-govermental spaceflight might be Blue Origin (i.e. a choice of Bezos of Amazon, rather than Musk of Xwitter). Although they're well behind on the practical successes, even against other launchers, they've got the progression from New Shephard (suborbital) to New Glenn (orbital) to Blue Moon (lunar... but where's the "New Armstrong" name?) fairly solidly mapped out.
Blue Moon is not a launch vehicle at all, hence no "New Armstrong" name, and they have had no huge successes with New Glenn yet because it hasn't flown.
Sorry, meant to convey that. Their development is 'more traditional' in that they don't cobble together "increasingly less unrefined" prototypes (forgive the double-negative!) in rapid succession, but more try to bang most of the dents out before "having a first go". But they've blown up far fewer New Shepherds than the various "flying watertanks" that SpaceX did on the way to similarly getting suborbital flights of Starship (which has never carried a human payload), but also now have that similar degree of reusable capability (
with 100% survival rate of its many passengers). Extrapolating that kind of progress to its New Glenn programme (never flown, but not short of applied development/fabrication), it's possible that (if they hit their November date for maiden flight), they'll have a Falcon-9 equivalent doing the currently proposed four flights for 2025 (still well behind Falcon flights, but well ahead of some other space
agencies) and be sending Blue Ring 'space-tugs' atop reusable Jarvis upper stages with everything from LEO to GEO and perhaps even some interplanatary probes.
Blue Moon is the whole thing, yes, but "New Armstrong" would be the logical name for their Lunar Starship equivalent landing component.
Blue Origin is somewhere between a bonfire fueled with money and a joke, frankly.
SpaceX is that with PR in overdrive and a "yeah, we meant to do that" attitude to failures and delays to their ambitious schedule. (Current ETA to Mars (unmanned) mission with Starship is a couple of years to set off just within easy transfer time. Maybe they will, maybe they won't, probably they'll have more than one setting off on a 'doomed' trial landing before the first has even proven it's not a completely bad design that should be revised on the next block of candidates.
Doesn't matter where the money comes from (deep founder pockets or the bleeding off from the everyday business of the founder's other newly money-making businesses), it can be burnt up (perhaps literally!) in R&D in ways both boring and exciting.
Hard to really put them side-to-side. As I alluded to, could easily be VHS/Betamax, once we have the future hindsight from the space-equivalent of bluRay or even Netflix times, but who knows which actually will be which... Or, Edison/Westinghouse, in competion (Westinghouse was proven right!) or Swan/Edison (Swan being left under-rated for his own developmental contributions) if there's any future collaboration.
Also, lol military Starship/all the Starship point-to-point proposals. Possibly, but hugely unlikely.
Proven accuracy to (near-)soft landing, as of FTS5. Quite possible they're only one or two FTSs away from doing that with a payload (should they desire to test that), and if they do the full five Booster/Starship tests a year then I can imagine a
crewed suborbital/FOBS-like flight and landing before the end of the second year,
if the dice roll well enough on the intermediate mixture of test-to-boom flights. They'll probably be catching both Booster (on return) and Starship (after a whole/functionally-whole orbit), intact, within the text two or three stackings if they don't spend too much time on anything else, and it's not incompatible with the need to prove the ability to do pretty much
exactly that with Lunar/Martian versions of the craft, just with subtly different balances of technical challenges.
If they can get anywhere halfway near their ultimate aim of 'colonising' Mars (which, in the short term, I'm not particularly an optimist about, but can't see any particular limit to how much effort they can expend towards this), they'll have automatically gained the 'side hustle' of intercontinental flight/delivery of (at least) bulk cargo. Whether or not they will ever be used to drop in the Space Marines onto the hotspot of the hour.
(What's more worrying to others might be the ability to send in an orbit-dropped ship equipped
only for very precisely arriving destruction. Imagine the conventional explosive-load you could hoist up, in amongst the routine Starlink-refreshing missions, then send down to land (or 'land') in the courtyard of any armed compound you want (or any other strategic target, not dug sufficiently far down into the bedrock) and wipe the entire vicinity off the maps. ...no sign that any of this is Musk's intent, except for his sucking up to the kind of ex-President who I'm surprised hasn't openly suggested he do it yet. But it's comparatively simple to do, given that we already have ICBMs plus now proof that we can scale up the system significantly.)