They each have their advantages. Wedi may be faster to get done, but in some ways isn't as flexible (in what you can do). In some ways, you can do stuff with Wedi you really couldn't do any other way, so it depends. For example, if you wanted a high fashion, scroll shaped, free-standing shower, it would be a pain to build conventionally or with Kerdi. But, you can buy a kit, glue it together, and be tiling it in less than a day with Wedi.
Kerdi is more flexible if you want a custom shaped shower pan. You can use their preformed pans (as you can with Wedi), modify them slightly (if it do it extensively, you'll have problems with asthetics, not operation because the bottom row won't be even if you cut things), but with Kerdi, you can save some money and make your pan out of the traditional deck mud (very inexpensive - mostly sand with enough portland cement to hold it together). With Kerdi, you can finish the walls with regular drywall, since the membrane is totally waterproof, the drywall is perfectly fine behind it. With Wedi, you can screw the panels directly to the studs.
With Wedi, the seams rely on you getting a good bead of their special urethane glue/caulk, and you have to seal the screw holes as well. Do a good job, and it's fine. Wedi also adds some insulation, so the walls/floor warm up quicker (same is true if you use the Kerdi foam pan). With Kerdi, it relies on you getting the proper overlap. Putting up Kerdi is sort of like putting up wallpaper, except there's no pattern to match, and you need the edges to overlap. You can get the overlap with either the full sheets, or (easier) use the thinner Kerdi-band material.
Cost wise, if you don't use the Kerdi pan, and 'roll your own', it would end up less expensive. If you use the Kerdi pan, Kerdi and Wedi are probably close to the same costs. Kerdi material is more widely available, so you have a chance of some price competition. Wedi is not well represented in this country, so your choices of supply may be more limited (depends on where you live). If you use their pan, it's about the same as Wedi. I think the Kerdi drain is more flexible and easier to use - it's more adjustable.
I've used Kerdi twice, and found it to work quite well. I considered Wedi on one project, but in that instance, Kerdi worked out easier. They had a demo near me on Wedi, but I couldn't get away from work to attend. I did get a chance to attend a school on Kerdi...very informative. If I'm lucky, they may do the Wedi thing again now that I'm retired, and I'll get a chance to see it first hand rather than in a video.
If you want a shower without the need for any caulk, Schluter also makes some neat expansion joints for the corners/floor seams. But, if your walls aren't very plumb, it can be a pain to use them.
Check out www.johnbridge.com for help and advice on tiling. And, both the www.schluter.com and www.wedi.de sites have a lot of info on their products. I think both of them have videos you can view to see their stuff being installed.