Either make will be 4500-5000 lbs dry once optioned. Once you add your gear and fluids expect to be 6000+ lbs. You may want to reconsider going with a Class 3 DRW and look at a Class 4 or 5 DRW truck. There are additional costs going with these larger trucks, so you will need to decide if this is best option or to look at a Class C type RV. On that same note: Are you sure the Stable Lift is rated for that kind weight? I'm not sure these TC's are constructed so you can lift them anywhere but at the corners and would contact EC and Host about using this type of lift.
It would benefit you to go to a RV show or dealer where you can compare these models side by side. There are definitely pros and cons to each manufacturer and model in which you show interest. Since these models require a significant truck to carry them and are more expensive, there are less of them on the used market and you will need to travel anyway to find the one that is right for you.