I think that in versus threads, Durability is often ignored even though it is the primary counter to Lifting Strength.
Tatsumaki's lifting strength cannot kill or crush a character who possesses extremely high 2-C durability, so there is no reason to argue that she can crush him to death or kill him through suffocation.
Furthermore, Broly is capable of traveling between planets and through space. This was stated in Dragon Ball itself when the Supreme Kai and East Kai mentioned that Broly was destroying planets across the Southern Galaxy and was close to finishing its destruction. This means that throwing him into space is not a problem at all, because he can simply return to Earth or travel to any planet within the galaxy. So how can it be said that he loses in space when, within a short period of time, he traveled across the planets of the Southern Galaxy and wiped out all life on them?
Broly's lifestyle is also somewhat similar to Frieza's. He is different from ordinary Saiyans in terms of upbringing and experience. Frieza, for example, can escape to other planets by traveling to them at high speed. Whis himself stated, when Earth was about to explode, that Frieza had undoubtedly escaped to another planet before the explosion.
Since BFR into space becomes useless if Broly can travel between planets, throwing him away is not a valid win condition. He would simply return immediately and unleash a full-power attack, such as the one he used against Gogeta. When Gogeta attacked Broly with numerous energy blasts from above, Broly gathered a massive sphere of power around himself and released it in every possible direction, wiping everything out instantly. Tatsumaki would not be able to escape such an attack because it covers all possible directions. Even with equalized speed, the energy blasts spread everywhere, leaving no room for evasion.
Additionally, according to the profiles, Saiyans possess considerable endurance in space. They can survive without breathing for a very long time. Therefore, throwing Broly a relatively short distance into space is trivial. He could simply disappear from sight and reappear near her immediately, or launch a finishing attack from space itself, destroy the planet, and then flee to another planet—just as he did while devastating the Southern Galaxy.
Broly wins.