Great thread!
I have a braun electric that I got for Christmas a few years ago from the Wife. I use it sparsely. At first I tried to use is regularly but kept going back to the razors to get a proper shave. The darn thing always left a few hairs, always plucked a few in the process, and always gave me more irritation than a closer shave from a razor. Operating costs were high too as the automatic washer needed a pricey fluid container exchange pretty often. Tried replacing the "cutting" element a couple times at significant cost with very little benefit.
Been using a mug/soap/brush method on a wet face for razor usage for years and definitely prefer it as there is better control over the lather characteristics and the brush is a fast applicator.
Favourite razor is certainly not going to win any awards amongst the shaving enthusiasts, but has proven to be the most cost effective way to get close shaves without nicks and cuts... It's a quad blade job sold under the Kroger "generic" brand name at the grocer. They come in 3 packs normally, sometimes "with a 4th free" packs are there. IIRC they are around $5 for 3 "quad" blades... The Money saving part comes from the amazing robustness of the razors used in them. They hold a "sharp-enough" edge to go ~3-4 months shaving twice a week. So yea... I buy about a pack of razors for about $5, once a YEAR and am happy with the results. Wife tried the feminised version of the same razors and discovered the same thing- far fewer razor replacements, She also goes several months on the same razor now. The company that makes these things is never going to get rich is they keep making such robust blades... Makes me wonder what kind of steel they are using. I had used gillette mach type blades for years before that, only to find that the blades only last a couple few weeks and were costly to replace. Not to mention, the cheapo Kroger cuts closer with less nick than the machs.
When shaving, I first give it a good once over everywhere to knock down the majority of it, then usually a once over in the opposite direction, then I use my non-shaving hand to feel around my face and find the "grain" of the hair and which way it is facing. I then shave into the grain anywhere where the first 2 passes did not catch it all. By the time I'm all done, most of my face will probably have 3-5 passes with the razor but there is usually plenty of lubrication still available from the shaving soap and there is no irritation from this. In fact, achieving that insanely close (it's like, below the skin close) shave seems to cause the least amount of irritation. It's when I'm in a hurry and do a half-way job or try to get by with an electric quicky that I get shaving irritation.
Oh.... and a shave using that method, will result in less of a "shadow" 48 hours later than just after using the electric.