As if he wasn't hard enough to beat, the Dragon Ball guide books --the Daizenshuu -- contain concept art for Broly that implies he could have had a tail. However, it seems that the production staff decided against this feature, as we never see Broly with a tail in any of his appearances up until Dragon Ball Xenoverse, in which Bardock uses Vegeta's Power Ball to transform into his Great Ape form. He then destroys it after in order to prevent Broly from doing the same, revealing that he had indeed kept his Saiyan tail. So, does the tail play a key role in Broly's strength, or was the inclusion in the game an oversight by developers?
The answer isn't simple, but there could be an explanation as to why we never saw Broly's tail up until that point. In Saiyan culture, it is common for the warriors to wrap their tails around their waists like a belt, not only as a fashion choice but also to prevent their tails from being grabbed. Should a Saiyan's tail be grabbed during a fight, it would render the Saiyan incapacitated, as grabbing their tails causes extreme pain. Wrapping their tails around their waists prevents this.
It is entirely possible that Broly still has his tail during his first fight with Goku -- it's just that we can't see it. He most likely has it wrapped around his waist and it's hidden beneath the sash of his pants. If we look closely at the sash he wears, at the very top, there is a part that sits above his golden belt; a part that looks like it's rolled. This could be how he's hiding his tail: wrapping it around his waist, then the rolling the top of the sash around it to conceal it from sight. Bio-Broly, the clone of the original Broly, is also has a tail as an adult, so this also lends credence to this theory.
If he does indeed have his tail, does that affect how strong he is or could be, then? Well, yes and no. When he was born, Broly was already more powerful than other Saiyans, having a Power Level of 10,000 at birth. Like all Saiyan babies, he had his tail, so it's unlikely that the tail plays a major role in how strong his Power Level is. On a physically destructive level, however, it could.
Combining the power of the Great Ape form, his increased Power Level, and his mental instability, Broly as a Great Ape would cause levels of destruction that are unimaginable. It took Goku combining his power with donations from his friends to defeat Broly; Goten, Gohan and Goku's spirit had to launch him into the sun another time, and in Xenoverse, it took Great Ape Bardock, the Future Warrior and Freiza Saga-era Vegeta to bring him down. Had he been given the chance to transform into his Great Ape form, it would probably be near impossible to stop him.
Broly also ascended beyond the Great Ape form as a baby. His strength would increase at a rapid pace never seen before. In the Dragon Ball Heroes: Victory Mission manga, Broly achieved Super Saiyan 4, meaning he also achieved the Golden Great Ape form. Again, it takes a combined effort to bring him down, even in this golden form.
So, it seems the tail just adds a more physically destructive aspect to Broly's strength rather than a Power Level increase. Since we have only seen his Great Ape form in side stories rather than canonical sources, it's hard to say how much more powerful he really could be. But since all Saiyans are born with a tail, it's unlikely that this is a major contribution to his power overall.
Should he transform into his Great Ape form while not under his father's control, he could definitely be more destructive, if only because of his size rather than abilities. But it seems that it only plays a minor role when looking at how powerful Broly is as the Legendary Super Saiyan.