No, What decides a particular transaction's priority is its included fee as the miners prioritizes transactions with a higher fee.
OP is talking about transaction priority, which has a formula including its coin age and output amount.
If A is bigger in size, Transaction B will most likely get confirmed first. But If they have the same size then luck will probably decide which will get confirmed first.
Why would the smaller be included first?
Transaction priority is mostly deprecated right now, the reference client does not use it for free transaction anymore. In fact, reference client doesn't consider priority when relaying transactions anymore.
You have to understand that miners have their own backend and it is up to them to decide which transaction gets included first. No one would know which transaction would get included first and its neither useful nor important. If I were to give an educated guess, it would likely be the transaction for which the miner sees first that would get a higher chance. The whole process about mining is not the miner finding a block and include the transaction. The inclusion of transaction is before the miner starts hashing their block header.