Very likely, a large holder will get the next 1-3 block rewards corresponding to the large chunks of ( and higher-weighted) coins assigned for the POS, immediately after he/she starts staking (minting), but once rewarded, the large portions of coins will no longer be eligible for staking until next time of days or weeks of holding periord for that portion of coins to be used again. There should be less input for staking as time passed, to the point that if you (" with the other wallet") just start staking at that point, you might have a higher staking weight to get the next block.

It is a matter of chance; therefore, your chance of getting rewards immediately starting staking is much, much lower, but even if both start at the same time, there might be a time say one hour later, the one having only, say 1/10 of total coin balance of the other wallet client, would have almost the same amount of coin weight to get the next reward which you are supposed to get anyway.

It might takes longer if there are many, many higher coin-weight wallet starting the staking during the time you are in.

As you can see, the one with extremely small amount of coin might not get a reward for quite a few months but by the time, you would have much higher amount of holding-time and staking power.