What would have happened if Balaram had joined the Kurukshetra war?

Who was Balaram?

To start with let's understand the nature of Balaram. Balaram, elder brother of Krishna was nothing like Krishna. Krishna was cunning, manipulative, knew exactly how to handle a situation and how to gain maximum from the situation. He was mastermind, a quality which was instrumental in success of Pandavas. On other hand Balaram was naive, honest, someone who wore his emotions on his sleeves. Krishna was completely opposite, in entire story of Mahabharat Krishna kept his cards close to his chest. For instance he could have told Pandvas about the truth of Karna but he chose not to (for obvious reasons).

Incident of Subhadra's marriage will make difference crystal clear.

We all know Duryodhan was favourite student of Balaram. It was natural for Balaram to think him as a prospective groom for his sister Subhadra. On similar line, Arjuna was close to Krishna and Krishna wanted Arjuna to be his brother-in-law. But Krishna never admitted it to anyone while Balaram was very open about his wish. In fact he sent a marriage proposal to Duryodhan for which even Krishna accede (rather, he acted that he is in accord with his elder brother). In the end Krishna managed to create a plan which ended up in the marriage of Arjuna and Subhadra, a thing that he wanted from a start. And he did it without hurting Balaram's feeling.

In the end we can conclude that Balaram was naive, honest, straight forward, someone who always looked for good in people (come on, Duryodhan was his favourite student!). Not to mention he was righteous and peace loving person.

Considering this it was quite understandable when he chose not to go with any of the side. He saw two families, for both of whom he had immense love and respect, fighting a battle which could have been averted.

Now coming to the question...

Why he would have joined Pandavas?

Honestly, I think this would have been a very tough decision for him. In most part of the story of Krishna and Balaram, Balaram had immense amount of trust on Krishna's judgement. Yes, there are some instances where he did scold Krishna for his manipulative nature but overall he knew that Krishna will not do anything wrong. Plus, I think deep down he knew that Yudhistir, Pandvas are on a side of Dharma so their victory was inevitable. So these can be reasons for him to choose side of Pandvas.

What would have happened if he had joined Pandavas?

For me he would have done something similar to what Pitamah Bhishma did for Kauravas. Both of them were in same boat, they are fighting against someone they love. So I think, in this case, Balaram, would have told Yudhistir that he will not kill any of the hundred Kauravs to which Yudhistri, someone who always gave respect to elders, would have agreed without saying anything against the will of Balaram. All those small small tricks and plots that Krishna used to kill Pitamah Bhishma, Dronacharya and others, would have kept hidden from Balaram as he wouldn't have allowed it. In the end outcome of Kurukshetra would have been same and having Balaram on Pandavas side wouldn't have made any difference to main story.

Why he would have joined Kauravas?

In my opinion strong reason would be his love for Duryodhan. From the beginning he considered Durydhan as someone who had a passion to be better (Duryodhan was jealous with Bhim-Arjun and wanted to be best at Gadayudha), someone who was honest with his thoughts and emotions, in a way Balaram saw some points in duryodhan which he always admired. In addition to that people like Balaram tend to have sympathy for underdogs (already mentioned, deep down he knew Pandavas will win the war) Hence I think his heart would have forced him to choose Kauravas

What would have happened if he had joined Kauravas?

I think here there are number of possibilities. But before joining the was I think Krishana and Pitamah Bhisma would tried to talk him out of the war. Pitammah Bhishma would have tried to convince him, how futile is to join kaurava and personally, how he is feeling being trapped. While, Krishna would have talked about righteousness and Dharma being on Pandavas side and would have forced him to take decision to not to kill any Pandavas. (Thing to be mention here is that Balaram was best Gadadhari of that time and had a potential to beat all five Pandavas)
In addition to this I think one scenario in the war would have played completely different. We all remember how Abhimanyu was killed by all Maharathis. (which was against the rule of war) Balaram would have opposed this and may be, just may be, Abhimanyu would have got fair chance to fight and would have killed one/two Maharathis before perishing.

Plus, the incident where Ghatatkoch (half-asura son of Bhima) was killing kurusena andKarna had to use his important weapon, Vasav shakti (given to him by Indra) to kill Ghatakoch, I think here Balram would have made substantial difference. Balaram had an ability to deal with Ghatatkoch and Karna wouldn't have to waste his only power against Gahtatkoch which means a fair fight between Karna and Arjuna! (Obviously, Krishna would have come with something else to lessen the power of Karna and eventually he would have got killed by Arjuna only)

However, in the end pandavas would have won the war anyways since they Dharma (just) on their side. Balaram would have stayed alive as no one had an ability to kill him in a war.