Yes, a 32-bit operating system will only be able to utilise about 3.2GB of memory no matter how much is installed.
A 32-bit operating system can only directly address values up to 2^32. In decimal this is 4,294,967,296, which through no coincidence at all is the number of bytes in 4 binary gigabytes. This gives us the limit of 4GB of memory which can be addressed. (Certain exotic 32-bit server hardware & operating system combinations could utilise >4GB of RAM by addressing the extra memory indirectly.)
But the RAM on your motherboard isn’t the only memory in the computer. So other things, such as the memory on your graphics card, need to be taken into account and deducted from the 4GB total (which is why [B]Dee[/B] can only give an approximate figure).
So if you wish to use 32GB & 64GB of RAM you must check if your motherboards support that much (and if there are any limitations on the type & configuration of the RAM when using such a large amount, which are specific to each model of motherboard), and you need to use the 64-bit version of Windows.
UEFI vs BIOS is not a factor. If one motherboard happens to support more RAM than the other, it is for other reasons.