Regarding the Lansky, it'll work. One thing you'll need to keep in mind, if you ever do a complete re-bevelling on a big and/or thick blade, it'll take some time. Patience is key. Lots of metal to remove, with the relatively small hones. The total surface area of abrasive on the hones makes a significant difference in speed. Same applies with the Sharpmaker; it's not ideally suited to heavy metal removal anyway, as the ceramic hones are small and not very aggressive in grit. Re-bevelling a big, thick blade would take forever on the Sharpmaker.
For day-to-day maintenance and relatively light touch-ups, either system will be fine. I use the Lansky for rebevelling smaller and medium-sized blades, and it's great for that.
And the Worksharp, being a powered tool, would obviously be faster. But, for the same reason, you really need to be careful you don't over-do it.
As for sandpaper, it's likely going to be my 'go to' sharpening method in the long run. The more acquainted I've become with it, the more I see it'll handle anything I give it. It's my favorite method for maintaining edges especially, and new bevels can be created quickly (LOTs of surface area in a 9" x 11" sheet of it). I respect the opinions of those who might not prefer it, but the capability of it as a sharpening medium isn't lacking, at all. It has some sizeable advantages, in many respects. As with any sharpening method, 99% of it is technique anyway. That comes with repetition and thoughtful practice.