Gentlemen, you touch on some good points, and perhaps I should clarify a few things. The comments about equal temperament could set off a long and not entirely pertinent discussion, so I'll separate my comments into two categories and try to be careful with the second. I should also mention that I used to own a Turbo Tuner (non-pedal model) but I don't now (I have a Korg OT-120). I did pick up a Turbo Tuner pedal for my guitarist brother last year -- he loves it, and I haven't come across a pedal tuner that can touch it for features, speed, or accuracy.
ONE: Is the Turbo Tuner (and presumably other true strobe tuners) audibly more accurate than the typical electronic tuner?
In my experience, yes: 1)I can light up the "green light" on your typical tuning pedal and keep it lit while I adjust an open string over a small but audible range of pitches. They can't all be right. 2) Some tuners, like the Turbo Tuner and my Korg OT-120, will let you choose from a variety of different temperaments (the Turbo will let you define your own temperaments as well). Set to check for acoustically pure (non-tempered) 5ths on a cello, there is still some slight "beating" between the strings when each is adjusted with the OT, and they need to be tweaked by ear to ring true. Doing the same with the Turbo Tuner, I found that the strings rang true. There were other little tests I devised to check the accuracy of the tuners against each other, but I'll leave it at that and say that I assumed the accuracy advantage observed in checking acoustically pure intervals extended to tempered intervals as well.
TWO: Equal temperament/various systems of tuning:
I originally bought a Turbo Tuner with the idea of using it for intonation torture/practice in my cello studies in school. With this in mind, the accuracy and immediate feedback of the strobe, along with being able to define your own temperaments and shift them to different tonics, were key selling points. I found, however, that while the Turbo Tuner tracked quickly and well, it hesitated in the lowest octave of the cello (the Korg was actually a little quicker to lock in there). Also, for all of the Turbo Tuner's advantages, it lacks a speaker/pitch pipe function. After playing with it for some days, I found the old method of practicing against different drones (aural feedback, as opposed to visual) more useful for my purposes. So, as a broke student for whom a single $100+ tuner was an extravagant purchase (let alone two), I returned the Turbo within the trial period and kept the Korg. The Turbo was more accurate, but the Korg better suited my intended use. Apart from an initial reference "A," I wasn't using it to tune my instrument, and I wasn't playing electric bass at the time.
Equal temperament is cool. Like most things in life, though, it comes with compromises. Sometimes I use it, and sometimes I don't. You'll never hear a choir sing in equal temperament, and I doubt you'll hear a string quartet play that way. Even good wind and brass ensembles will tweak intervals up and down to make chords ring more in tune. I'll tune my cello slightly differently in different circumstances, but I don't use "regular old equal temperament". Tuning each 5th 2 cents flat on a cello just sounds terrible. Even a well-tuned piano isn't tuned that way: the octaves are "stretched" in order to make the harmonics of different strings line up better, and the amount of "stretch" varies with the piano. A well-tuned, 11-foot concert grand will be tuned differently than a little Yamaha upright.
All that said, equal temperament can work well for electric bass with keys, etc. When I show up for a jam (which is where most of my electric bass playing takes place these days) I'll usually either grab an "A" from the keyboard player and tune by ear or, if there's a tuner handy on stage (and particularly if it's noisy), plug into that and tune my open strings with it (not just one as I mentioned before). I still check/tweak by ear afterward. Unless it's really noisy, I'm faster by ear than with a pedal, and I am almost always done well before the guitarists staring intently at the floor as they tune their instruments (and, to my ear, better in tune).
If I start gigging regularly on electric bass, I'll probably invest in a tuning pedal, simply because some environments aren't conducive to hearing yourself well. If I do, it'll be the same Turbo Tuner pedal I got my brother (it's the only one I've come across that I would trust for tuning "silently" w/o double-checking by ear).
In the end, I think you should do whatever you're comfortable with that reliably enables you to sound good in your given playing situation. I'm comfortable tuning by ear, but I usually carry a tuner in my gig bag and I don't go up on stage with my instrument way out of whack. For the OP's stated goal of setting the intonation of his instrument, I think any good tuner would be a big help. I would take one with an analog needle over one with an LED display (watching its movements as you switch between fretting the note and playing the harmonic can help you home in), and would take the Turbo Tuner over either.
