hey steel! i just picked up on this discussion... great topic! I'm not sure about the WEPS, looks neat, but I do have extensive experience with the EP (both the apex and pro model). Trust me when I tell you you will love it, and I will probably have mine till I die! It has tons of options that allows you to highly customize your edge, from ~7 degrees to ~35 degrees (these are off of the top of my head so don't quote me here), and all the way up to a sub micron polish. I use the EP to sharpen straight razors (given, I do finish on a strop), and its no laughing matter what they will do (easily pass the hanging hair test and sever a hair in mid air).
I started off with the EP apex (you can pick one up for $130-150) and it comes with a lifetime warranty and GREAT support from it's creator, Ben Dale. You can call him anytime he's open and he will spend as long as he needs to on the phone with you answering your questions and giving you support.
stones are pretty cheap with the EP too... $8/stone and $5/blank for a total of $13 if you want to mount it yourself like I do to save money (extremely easy to do). You can re-use the blanks many, many times.
Kom is right, they hold their value great and resell WELL. after i had my apex for over a year and sharpened over a couple hundred knives on it i sold it on Ebay for around $130 (new one is about $150) and upgraded to the Pro model, which i'm loving.
using the EP will take you about 10-15 minutes per knife probably, depending on how dull it is and how comfortable you are with it. the only things i have had trouble with is that it doesn't sharpen serrated knives well, or ceramic knives (even if you get the recommended diamond stones/tape, they don't work). lastly, if you want to sharpen recurves, make sure you get the recommended stones for that or you will run into trouble. it won't sharpen convex edges either (which are a pain in and of themselves

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i have really grown to love the paper wheels recently however.. they have made my life so much easier! (since i sharpen so many knives) and they do an amazing job as well. they are OUTSTANDING on serrated knives, i can't say that enough. the paper wheels are the most efficient, best way to sharpen serrated knives out there as far as i'm concerned. but enough of that, you don't want electric =) so sorry for ranting about them. i just wanted to let you know what i have found has worked well for me so that later down the road you can look into them.
hope the above info helps! that's what i'm here for. holla at me if you need any tips.