A wide fit trainer exists to solve one problem: the bit across the ball of your foot where a standard shoe pinches, bulges your foot over the sole, or leaves you undoing the laces half way through the day just to get feeling back into your toes. It's not about going up a size, which just gives you a shoe that's too long and slops at the heel. It's a different last altogether, cut broader through the forefoot while keeping the heel snug, and if you've ever bought a normal trainer a size up to cope with width, you'll know that trick never actually works.
The difference between a good pair and a bad one shows up fastest in the stitching along the sides and in what the upper is made from. A cheap wide fit trainer is often just a mesh upper with more give in it, which feels fine in the shop and then stretches further within a few weeks, so the shoe that fit well in April is baggy and shapeless by July, with your foot sliding about inside it on anything other than flat pavement. A properly made one uses a firmer, structured upper, sometimes with a bit of leather or suede in the panels, so the width is built into the shape rather than relying on stretch, and it holds that shape for a year or more of regular wearing. Look at the stitching around the toe box and the eyelets too; loose threads or eyelets that pull away from the fabric after a few wears are a reliable sign of the former. Wipe them down rather than machine washing where you can, and let them dry away from direct heat, since a radiator will warp the sole faster than almost anything else you can do to a trainer.
Where they fall short is anything that needs a sleek line, a pointed toe, or a shoe that disappears under a tailored trouser. Wide fit trainers are honest about their width, which is exactly the point, but that means they look clumpy under slim cropped trousers or anything cut narrow at the ankle, and they don't pair well with anything delicate or going-out, a floaty dress or fine fabrics just highlight how solid and practical the shoe is next to them. They're built for jeans, wider leg trousers, or just trainers doing what trainers are for, which is getting you through a long day on your feet without your toes going numb by three o'clock. What they won't do is make a narrow-shoe outfit work, and no amount of good construction changes that.