Could anyone please advise which is more natural and if there's any difference in meaning in these two sentences?
I left early to make sure I would have an allowance and wouldn't get stuck in the traffic.
I left early to make sure I would have an allowance and wouldn't be stuck in the traffic.
If you can be X, then you can say get X to express you (or someone else) are transitioning into state X. Often you can substitute become.
Once you are X, you have got X.
Traffic can be looked at from multiple perspectives. Bad traffic is something that can surround you, and therefore you would be stuck in it. An area of bad traffic is also something you can enter, and therefore you would get stuck in it.
So, it's two ways of expressing the same thing, though get stuck leans more toward implying you are willfully entering already bad traffic, versus traffic becoming bad as you travel.