How useful is the stropping stage in sharpening knives?

I'm trying to choose between these two options

Stropping is very important, as it realigns the edge after sharpening or simply after use. After sharpening, besides realignment it removes small particles and irregularities, weak parts from the edge, making it stronger and sharper.

Actually, recommendation is to steel or strop the blade before each use. The edge gets deformed on microscopic level during each use, and if you strop or steel right after use the metal goes back to deformed state in few hours, due to metal memory effect. Which is why stropping or steeling before using the knife is far more effective.
BTW, that is what barbers do with their straight razors, stropping them before using it and during the use too, because razors are very thin edged and not very hard either, except for Japanese straight razors.

Here's a macro photo of the edge before and after stropping, clearly showing the effects of stropping - http://zknives.com/knives/knimgtmpl.shtml?/images/knives/macro/sestudy/wtnbnkstrop150x01.jpg

So, having said all that, I'd recommend getting a separate strop or a smooth steel. Both do exactly the same job, realign the deformed edge. If you get the steel, make sure it is a smooth rod, not the grooved one, which does more damage than good.

As for the electric sharpeners, the common problems with those are that the angle is fixed, which is probably ok for a lot of people, but another problem is burning the metal.
Wheels spin at high speeds, so if the operator presses too hard or too long the metal gets overheated and looses tampering.
Which means the edge will bet dull a lot quicker.

More expensive, newer electric sharpeners have built in mechanism to prevent burning the edge, while cheap stuff doesn't.

If I were you I'd make sure the cheap version has burn protection and get that plus a smooth steel.

If it doesn't then up to you to decide if you want to risk your expensive knives.

Here's more about stropping and steeling - http://zknives.com/knives/sharpening/steeling.shtml

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