The correct form of the sentence is the second one because. . .because you can't passivize intransitive verbs!
Let's take a look at Dictionary.Reference:
Develop: verb (used with object) 1
- To cause to grow or expand.
But is this the meaning the sentence is trying to convey?
The data that can be easily gathered from mobile devices can open new research opportunities which would not have been possible to develop with existing built-in systems.
As you might have noticed, here develop isn't to cause to grow, but is supposed to mean
Develop: verb (used without object) 2
- To grow into a more mature or advanced state; advance; expand:
She is developing into a good reporter.
- To come gradually into existence or operation; be evolved. - Dictionary.Reference
(emphasis mine again)
So, the meaning you were trying to convey in this sentence was the intransitive develop; which can't be passivized due to obvious reasons. Thus, the sentence must use the active voice.
That being said, you also have another option here: Delete "to develop" altogether! The remaining sentence makes perfect sense and looks a bit simpler:
The data that can be easily gathered from mobile devices can open new research opportunities which would not have been possible with existing built-in systems.
1: A.K.A transitive
2: A.K.A intransitive