This is going to sound mean, but the harsh reality is that if you don't get funding the first year, the chances of getting funding from the school in subsequent years is extremely low. Schools allocate GTA lines/funds to bring in new students, not fund students who are already in and paying their own way. Once you are in and paying, they are not going to give you a GTA position, no matter how good your work is. It's not about performance. It's about economics. If you're paying, they will use the money to bring in someone else because they know you're stuck--they know you can't transfer PhD programs easily. So if you commit to School A, you should do so only if you're prepared to pay your own way for the full PhD, and that seems foolish since you have a funded offer to another school.
I saw this very scenario play out at my school this year. A student was admitted to my program last year, but applied after the funding deadline. She was told she was a good candidate for an assistantship and encouraged to apply the following year. So she entered the program and paid for the first year. When she applied for funding the next year, the administration would not approve her for a GTA spot because she was already in the program, and GTA lines are dedicated to recruiting new students, not keeping existing ones. This student got screwed and she doesn't even know it. I was taken aback at this process, and I asked around to some other friends who work at other universities. Their response has been universal: this is how all of their schools function.
With this in mind, I would urge you not to engage in the sort of thinking that lets you rationalize that "If I excel in the first year, they'll give me money in the subsequent years" because realistically, that probably won't be the case. The funding process is not a meritocracy. I think you've got a good option in School B, with the possibility of funding throughout.