Rather unhelpfully - the one that works best for you!
First question to consider is what type of grind is on the blade (s) you wish to sharpen - is it a flat type or convex. A convex can be touched up on a flat system, but in time you will basically turn it into a flat edge.
The second point to ponder is to be clear in your mind about what needs to be done to a blade to produce a sharp edge. Definitions vary, but if we assume sharpening is an abrasive process that removes metal and honing is a non abrasive process that removes inconsistencies and burs. I appreciate that isn't precise, but really only heading for next bit -
Even as a sharpener retailer, I believe most knives are over sharpened and under honed. The amount of blade metal that gets ground off knives annually is probably all that keeps the knife industry going!
Ever sharpened a knife and it felt like the edge was so 'good' in grabbed your finger print? Yet when used the edge dulled very quickly. Chances are what you felt was a fine metal 'feather' or bur created by sharpening. It is very weak and upon use breaks or folds readily - creating a dull edge.
Notice how chefs and butchers spend a good deal of time with a 'steel' on their knives, but far less often do you see them slaving away on a stone.
Sharpen to set your edge, hone to maintain it.
I like the Lansky 4 rod box we sell ( declared bias here ), it will sharpen and also semi-hone. Spyderco Sharpmaker does the same thing. As a type of system, our experience is they are one of the most useful - for most stalkers. There are lots of good products - I'd never wish to start a 'this is best' debate, because I don't think there is any one single answer.
The most common issue is using a stone or other abrasive that is too coarse. Little and often is the best approach. Many commercial products - even when listed as 'Fine' or 'Extra Fine' - are really quite coarse. For a quick thumb test they feel great - because they are effectively producing a serrated edge. The finer and more polished your edge the better it will cut deer and all else being equal, the longer it lasts.
The Carbide type handy sharpeners tend to produce feather edges - so shave rabbit skins just great at gamefairs, but remove heaps of metal and can damage hard edge blades through chatter.
There's little to beat getting hands on with a few different products and see what works best for you.
It would be interesting if you could let us know how you get on.