The Alweld Flat LA 2013 is a flat-bottom design and the Alweld Vee DSLW 2013 is a modified-V design, so you're likely deciding between two noticeably different on-water experiences. Hull type shapes everything from ride quality and fuel burn to dock handling and resale trajectory.
For family outings this is probably the sharpest distinction between the two. The Alweld Vee DSLW 2013 is rated for 6 passengers, while the Alweld Flat LA 2013 caps at 5. If you're regularly pulling extended family or a group of friends onto the water, the extra seats on the Alweld Vee DSLW 2013 could be the deciding factor.
Bottom line: Choose the Alweld Vee DSLW 2013 if your priority is putting more people on the water - it handles 6 passengers and at 12,0 ft it has the deck room to back that rating up comfortably. The Alweld Flat LA 2013 is the smarter pick if you want a lighter, easier-to-trailer boat rated for 5 that costs less to run day-to-day.