I have a pretty large tc its a real lite 1200 that weighs about 3900 dry I have had it on a srw truck while it hauled it ok stability and safety are unmatched compared to my drw truck.
the previous owner of my camper hauled it on a srw truck and said it did fine but I wasn't comfortable with it. Day and night difference in a dually. Now I can tow my boat and use my camper like I want to. If you don't have a truck yet and can spend the money for a drw you won't regret it.
I jus bought my dually and I was comparing prices on srw vs drw before I bought miine and in my area it wasn't a whole lot of difference in price on used trucks, now new trucks that's a different story