Wow. Looks like I started a whole conversation here. I'll reply in rapid-fire fashion with my 2 cents before moving on to my photo of the day.
There is a rather big difference. Lenses built for AF (like most modern lenses) have a focus by wire system for MF (meaning it's not really responding to your touch/feel, but rather, your rotation of the ring causes an electronic signal to move the focus inside the lens. These lenses, meant for AF, have a usually short throw (the amount of rotation of the ring that takes you from minimal focusing distance to infinity), so the focusing feels kinda loose and imprecise (hard to explain in words). The slightest touch to the ring will take you from say 3m to 10m (just an example). Manual lenses are designed to have an actual dampened ring, with usually pretty long throws as they do not require to communicate with an AF mechanism and are meant to be fine tuned by hand. I hope that made sense.
Also, as some mentioned, there is an inherent satisfaction in controlling the focus yourself. Much like the feeling you get from going off the "Auto" setting in your camera and using M for the first time. So there's definitely something of a "fun factor" to the experience that also causes you to slow down and think about your shot before hitting that button repeatedly.
AF does have its advantages though. There's no way I could ever MF in time to catch birds in flight, sports or wildlife.
Exactly what MacRy said. I explained the technical difference of MF lenses. But there's something more to it than that. A bit intangible (albeit visible in photos).
These lenses are usually very small. Which makes carrying them around fun. And makes the shooting experience more fun. I have started taking my camera with me almost everywhere I go. You never know when something interesting will lend itself to a photo. Big difference compared to the more rigorously planned approach of "going for a photo walk" where you intentionally set out with 10 lbs. of gear (for me, that meant the Canon 6D, 16-35L, 24-70L, 70-200L and sometimes 100-400L)...Yeah.
As for character...Well, that's another one that people who haven't tried it seem to think "How can something based in physics have character? It's not really organic". And that is indeed true. But after trying a couple of these lenses (an old Canon FD 50/1.8 and a Vivitar 135/2.8), both of which practically fit in my pockets, I do understand what character means. Character really means "lack of technical perfection" and that can be a good thing or a bad thing, depending on one's interpretation and how one chooses to use it.
Modern lenses are very much striving for optical perfection (and many of them are pretty damn close). That means sharpness from corner to corner, microcontrast across as much of the frame as possible. Resistance to flare using modern lens coatings, etc.
Basically, the type of things you read about as "pros" in every new gear release pamphlet and announcement.
Older lenses don't always hit those marks. Some have pretty bad contrast, or bad flare resistance. Or their colors are rendered somewhat differently, or get soft away from center-frame. All this contributes to each of these lenses producing photos that are a bit different and distinct from "technically perfect" stuff we see in most modern lenses.
That can be good in some cases (some lenses are said to have "character") and it can be bad in some cases (some lenses are just awful).
That shot I posted yesterday...Very minimal processing. I don't think I could have gotten those colors and that vintagey look from my Canon (at least not without post processing it to intentionally look that way).
Here's today's photo. Shot with the Canon FD 50/1.8. Handheld and manually focused at f/1.8 for that uber shallow DOF.
Also note that this lens can be had for under $100 on ebay...(to compare to those Leicas mentioned in the above post, hehehehe).
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