Just because you used the same number of strokes on the edge doesn't mean there isn't a burr. There are too many variables like the exact sharpening angle, pressure, bevel being thicker on one side, ect. It sounds to me like you have a burr problem, there is a sticky at the top of the maintenance forum that tells of microbeveling. Microbeveling is your friend, if you are trying to get a razor edge on a single bevel only, it can be very challenging and you are probably working much harder than you have to. Microbevels also help get rid of stubborn burrs which tend to flop around on softer steels such as the machete.
To apply a microbevel, sharpen as usual except just get a good working edge with a medium/fine stone, don't worry about getting the edge perfect at the moment and don't waste your time polishing. After you get a nice thin primary bevel, increase the angle at which you sharpen several degrees, in other words lift the blade spine up more for a more obtuse edge angle, use your fine stone for this (the Spyderco might be a little too fine if you have a large burr, I would stick to the Arkansas or white sharpmaker rod for this task) and give each side a couple of strokes using very light pressure, you can check to see if you have a burr left by seeing how the edge bights into your thumbnail or other hard object, if it bights harder on one side than the other, you have a burr on that side though it will probably be very small. You can make another very light pass on that side, or you can strop it true with a piece of leather.
I have been freehand sharpening for years and a soft or hard Arkansas stone with a microbevel gets all my knives hair popping sharp,and they stay that way for quite a while. Don't let people tell you natural stones aren't good for sharpening, I have lots of sharpening equipment including jigs, diamond stones, ceramics, and other devices and prefer my Arkansas stones dry any day. They have great feedback and leave an awesome edge in capable hands. Sounds like you are on the right track, just give my technique a shot and let us know if it helps. You are also more than welcome to shoot me an e-mail if you want to ask me any questions directly. Good luck and keep asking questions, this place is a wealth of information.