Hi b-man, well I have around 60 hours in the PA38 and around 30 in the PA28 and my question to you is this, how tall are you?
The PA28 was not designed with short people in mind, the brow panel is set very high and sitting on a cushion doesn't always help. I'm 5'7" and it is a real pain in the neck to manoevere on the ground because of the poor visibilty out of the front. Even in flight you might find yourself stretching to see what's going on.
In terms of handling, the PA38 is twitchy and very sensitive to turbulence, I've banged my head on the canopy from being shaken around
Having said that it is a good simple aircraft to learn on and it helps keep the costs down.
Apart from the high coaming on the PA28 it is a better looking aircraft and smoother to fly but more expensive. A good solid cruiser. However the twitchiness of the PA38 can help to train better stick and rudder skills.
Phil