Back in the day when recording consisted of dragging a bunch of rust stuck in plastic past a magnet, punching was a very common technique to fix mistakes. When DAWs matured, it seems comping and working with bits of audio on multiple tracks became more common.
 
I had neglected punching until I was doing a project with someone who used Pro Tools, and he did a lot of punching (BTW he has since switched to Sonar and is much happier). So I've been thinking about when to comp, when to punch, and when to combine the two...and I've come up with a workflow that seems viable. I offer this NOT as a "this is the way to do things," but rather, because others might find it helpful or have suggestions for improvements.
 
1. Start off with comping. However, if after recording a few takes I think I mostly have the part down, then as the comping continues I'll sing or play only in the parts that I think need improvement. This kind of combines the mentality of "punching" with comping, because I concentrate on a specific section that needs work, even during the comping process.
 
2. Edit with speed comping and create the part. If all is well, then I'm done. But...
 
3. If after listening back there are one or two things that bother me, I'll punch just those changes on the otherwise "finished" track.
 
This seems to be the most efficient way for me to work. But I'm always up for trying new ways to do things, so if anyone has comments on punching vs. comping, I'm all ears.

The way the comping works in X3 I never do punch tracks anymore.  I just feel you have more control with getting the clip to sound natural on the track with the control over cross fades.
 
I think essentially workflow wise the process is near the same.  Doing punch tracks I'd set the punch points and start playing along so it would flow naturally.  Usually where I'm punching would be coming in an out of a fill or something like that, so I'd set the punch points to give a couple of measures buffer.
 
Honestly now it's just easier for me to setup a take lane and start the recording in the are where I would need to punch and then use comping afterward.
 
This has been such a time and lifesaver in X3.  To be honest the take lanes never worked properly in X2 for doing multi track drums, and there was no speed comping, so trying to hand edit that was a pain and often didn't work correctly.

This is very close to how I do it, myself.  As I keep saying, the new comp method is the best work flow improvement that CW has made in a long time.  But, even the ability to punch in at precise points is way better than what we had with tape.  In order for tape punch ins to be gapless, a minute section of tape was erased to avoid the pop or click which would occur without this.  This made pure precision punches impossible, as one might erase a section of the track that was being fixed if there were no gaps in the signal.  Digital fixed that a long time ago.

I am too lazy to punch anymore with digital. With speed comping I prefer to record a couple bars before/after a "punch point," then I can decide on the splices (the punch points may not be ideal after the fact).

I've gotta admit..I tried comping exactly once. My computer gagged and crashed.. So I only do the punch (the past way of manual punching by hitting the record button by hand has ruined many a track. We have a much better way now) With that said, I'm also guilty of mixing and applying many effects while also tracking, especially while doing overdubs over several days of recording. I'm sure I was asking for a crash. I may give it another go soon, on a clean project of say 16 tracks of audio, to see how my machine handles it.

What about if you are not recording yourself but an artist who is on a bit of a time frame.  Punching may be better to do first in this situation especially if it is an obvious thing that needs to be corrected rather than just trying to get an alternate take. Alternate takes are better to put into layers and comp later.
 
I was recently involved in a 2 day session as a drummer and they were running Pro Tools.  We tended to punch in and fix things right then and there.  It seemed to work out much better at the time.  The good thing about it is the problem area is very fresh in your mind.  It means now that particular lane is correct all the way through. We did alternate takes of course for comping options later.
 
Maybe it is a Pro Tools thing punching in and out. Studio One makes it very easy as well.
 
I was a bit surprised they were doing it so much on this session. It is a bit like VU meters, maybe we need to bring them back too!
 
I think it depends on the caliber of the musician involved as well.  If you are dealing with a very skilled player then a punch in is quick and easy and they are going to nail it first time around.  I think it could work very well in that situation.  But recently I was recording a vocalist who was a bit unpredictable.  She would have not handled punching well at all.  The best and fastest way for her was to just keep doing layers. In fact in Studio One I was looping over sections and just recording takes to layers which is a very cool feature.  I got the vocal take I was after by comping later. (and using Melodyne a lot too!)
 
But on another session I was working with a fantastic singer who would sing 99% of a take perfectly and maybe make one little mistake. I punched that in at the time and she nailed that perfectly of course. It means that particular layer is perfect all the way through, no time wasted later fixing little areas of concern.  We did another take on a new layer and maybe punched in or two spots but that layer also ended up perfect.  Comping was now just down to artistic aspects rather than repairs.
 
Good point though Craig.  We should not necessarily abandon things we did in the past just because we have alternate ways of doing things now.

Once I get a fairly good comp sands a couple niggles, especially with harmonies...I'll just loop the areas needing work and comp some more. Super quick.
 
Isn't that what you're saying? Way more easier than punch in/outs
 
I love that part... vamp on the entire song, for emotional consistency/melodic spontaneity  then mini comp areas still needing work...it's wonderful and way quicker 
 

Vastman
Once I get a fairly good comp sands a couple niggles, especially with harmonies...I'll just loop the areas needing work and comp some more. Super quick.
 
Isn't that what you're saying? Way more easier than punch in/outs
 
I love that part... vamp on the entire song, for emotional consistency/melodic spontaneity  then mini comp areas still needing work...

Not quite what I'm saying. By doing a punch, if I get it right, it's done. If I comp, then I have to evaluate each take. Another issue is the "vamp on the entire song" aspect. With a punch, I can roll back and get into the groove prior to the punch. If I set that point as a comp, it's going to go back to the beginning each time and burn up time...but if I just comp a short segment, then I don't get a chance to "warm up" prior to that point.
 
To each his own, though! I like software that allows multiple workflows so you can choose the right tool for the right job. For example I'll often comp a short segment if I'm not trying to get a part "right," but trying out different approaches to hear which one I like best.

I guess I can understand mimicking the groove you were in before a punch point.  I guess I never had a problem with that because I went in with the same mindset as a punch track.  I know where the mistake is and I'm concentrating on that point.  For me comping just gives me much more flexibility.  Let's say I hit a clam  toward the end of a two bar fill.  With doing punch points, I might go back and mess up the beginning of the fill, but nail it at the end where I needed to fix it. With a punch track I have to go back and do it again.  With comping I can usually comp in the first bar of the first take and the second bar of the second take.
 

I don't really punch but record the "new version" of a problem part. As far as I've understood Cake's comping record mode, this means it automatically comps it in to the listening take. Yet I can still easy switch back and compare. Not that I do very often but I've just not really seen the need for punch when using this mode.