To add a few more thoughts on the Big Three:
NG only makes solid rockets, and that only since they bought out Orbital ATK. Their only liquid system, Antares, is a frankenrocket that uses a Zenit first-stage core built in Ukraine and the RD-181 from Russia, with a solid second stage. Therefore, they don't make their own liquid systems. However, since they now include Orbital ATK and no one else really does it nearly as much, NG is probably THE place to go at this point for a (non-hobby) solid rocket.
LockMart has the heritage of the Atlas, but again, they don't make their own engines anymore now that the Atlas 5 uses the RD-180 from Russia. They are buying out Aerojet though so this may change, however no users have emerged for the Aerojet AR-1 engine, which is basically just an American-built RD-180, and NG's GEM boosters were chosen over Aerojet's boosters for the upcoming ULA Vulcan. However, the RL-10 engine isn't going anywhere with upcoming use on the SLS and continuing use on Centaur upper stages.
Boeing's last few years have been marred by a few colossal, public screwups with the 737-MAX debacle and the Starliner test flight. The rocket that they built which ULA inherited, the Delta 4, is being retired. SLS was slammed by the GAO as being over budget and behind schedule because of poor management (though whether this is more NASA's or Boeing's fault is not clear to me).
Also worth noting about all three, aside from NG's solids, none of them have as much "vertical integration," i.e. make as much stuff in-house, as SpaceX and RocketLab.