If you are trying to lose weight, use the one that tastes the best to you. I don't particularly care for the taste of sucralose so I use aspartame (though my fave is cyclamate but I havee to order it abroad and that's a BIG minus because it costs a fortune to ship.)
Both are safe and good diet aids. I think aspartame might be a tad safer because it's been around longer and has been used worldwide in trillions upon trillions of doses.
The internet horror stories are well paid for by the sugar industry which thinks no meal is complete without several tablespoons of sugar! They should include vials of insulin with their half sugar/half grain breakast cereals!

The cancer scares are all made-up twaddle.
Virtually every major health organization world-wide has signed off on the safety of aspartame.