Strange, the Desire has double the RAM and the same amount of onboard memory as my TP2... but I have no RAM problems, and WinMo is far heavier than Android (Android runs just fine on it too).
Do you have an SD card? I have an 8GB in mine, and install most apps to the SD-card, thus leaving the phones internal memory free and ensuring problem-free running.
If it is forcing the closure of programmes, that is strange to be related to storage memory, though not unheard of (you could be having issues when an app is trying to use SWAP (linux version of the pagefile) or the /tmp folder whilst carrying out tasks), and is more likely to be related to RAM usage (though having said that, Android runs on Linux, and Linux is extremely efficient at handling memory designation).
If you dont have an SD card installed, it could be worth trying it, and moving some of your larger apps across to the memory card (this will involve unistalling the apps and re-installing them).
Stupid really how modern-day smartphones dont have 2GB onboard storage memory as a bare minimum, given the realative cost of modules being pennies.