In general non synchro trans have more room for wider gears and are stronger. One of the problems with street driving a dogbox that I didn't think of earlier is whatever gear you go for, it goes in. So if you go from 3 and miss and go for second it goes in second with little effort. Many people with H patterns have lost bottom ends due to this. So you have to be careful all the time. Wheras most synchro trans have a lot of resistance trying to go back into second from a high rpm shift out of third. Also you can't baby shift a dogbox. You have to go for it quick or you risk rounding off the dog engagement teeth.
So, like I said earlier its fine for a weekend or couple times a month going to work car. It seems that at some point cars that you race become bad daily drivers. You add a cage, dogbox, cams, etc...