The Touch Dual has the Qualcomm® MSM 7200, 400MHz
and the Touch has a totally different processor TI's OMAP™ 850, 201 MHz
The Mogul is a Qualcomm 7500 400Mhz which seems about the same and the Touch Dual's. If the processor's were faulty, i dont believe HTC would continue to put the Qualcomm chip in any device they sell. They surely would have updated their website, and we would be hearing about this everywhere. I say Myth Busted!!!!
http://www.htc.com/product/03-product_htctouch_dual.htm
http://www.htc.com/product/03-product_htctouch.htm
Links for Comparison