You use both – with significant and semantically essential differentiation in the point of contact between the tongue and palate or teeth.
Exactly. We have the capability to express a wide range of effects, depending on what we want to express, and there is plenty of overlap among them too.
For example, while the tip of the tongue may give us more control over the precision of the timing of the attack on a note, say, (by virtue of being later in the vocal tract than the throat) we can choose to soften the action of the tongue in order to mimic the sound of a glottal stop, if we choose to.
I think the way we play wind instruments is quite analogous to the way we speak, and this has been recognized for a very long time.
I think the authenticity of the music we produce is determined a lot more by when and where we choose to use articulation, than it is by the precise mechanism we use within the vocal tract to generate it. I think the similarity of sound among players that use different mechanisms in their vocal tract speaks to this fact.
Players like Aoife Granville and Mary Bergin utilize a lot of tonguing, but still sound authentic to me.
Conal Ó Gráda’s ‘pulmonic egressive’ reminds me of something possibly of relevance to the OP that I had thought of listening to Michael Eskin’s examples. Air flow has not had a mention in this discussion but in my experience it’s another thing (the one already mentioned being finger coordination) that can be useful to practice with no tonguing. To get the right pitch we have to get just the right amount of air through the windway. For big intervals between notes it can be quite a big change. Tonguing adds a complication.
Though I’m sure their are those who insist everything must be practiced at the same time.
Wow, long thread. I didn’t read every reply, so this was probably already mentioned, but just in case it wasn’t…
The suggestion for playing with straight fingers is probably so that if you decide to play low whistle or pipes at some point, you’ll already be used to it as, unless you have very large hands, you’ll need straight fingers to cover the more widely spaced holes.
While I tongue more than most, tonguing every note (for any musical style) is probably a bad rule to go by. 
-Brett
I often hear the terms “glottal stop” “tonguing” and “breath push” used apparently interchangeably, with “glottal stop” often not seeming to refer to what it does in linguistics.
Musicians often seem as unaware of the mechanics used when playing as people in general are of the mechanics used when speaking. It would be cool to see what’s actually going on.
I didn’t realise that.
I tried to explain to a newbie that there are various ways of interrupting the air flow, but in reducing order of hardness, the main ones are T-tonguing, K-tonguing, and the glottal stop – which I described as like saying the word “better” without any Ts. That’s standard pronunciation in large parts of Britain, so it comes very naturally.
Nice articulation of the three. 
OFF TOPIC: it drives me nuts when TV readers say “coo-ent” instead of “couldn’t”. Sounds lazy and juvenile. Grumble grumble.
In Yorkshire, “couldn’t” is indistinguishable from an unprintable slang term for female anatomy. People say it all the time and nobody bats an eyelid. 
I think the advice to tongue every note is absurd. My advice would be to buy Mary Bergin’s whistle tutor which comes with CDs and is absolutely meticulously done. She is an insanely good whistle player and is very good at imparting her knowledge about how to play Irish music on the whistle. She goes through ornamentation and tonguing in great detail amongst many other things. I had the experience of being in one of her group classes and again, she was absolutely meticulous as a teacher. No one else can touch her in my opinion and I don’t think there would be another Irish music tutor out there that would be anywhere near as good as the three volumes she has produced.