I'm less interested in the mechanical value of an integrated headset versus a traditional headset. I'm more interested in what an integrated headset means to the geometry and aerodynamics of a steep-seat angled tri bike, and it can mean quite a lot. That's the theme I'll explore, and I'll do so a few paragraphs below. But first an description...
With a traditional headset top and bottom headset cups are pressed into the frame - into the top and bottom of the head tube. An integrated headset is one in which the cups are no longer present and the bearings pop into the frame. The head tube itself is reamed and chamfered so as to take on the utility of the cups - they are the cups.
The nice thing about an integrated headset is that about two centimeters of "stack" is no longer there. This might be a big deal if you're between 5'9" and 5'11" or if you're shorter than, say, 5'2".
I'll give you an example. Let's say you're 5'9" tall and your road race bike is 53cm. Your road bike's head tube might be 13 cm in height. If you want to ride a tri bike with 700c wheels, you've got to drop about 5cm from your head tube length, because tri bikes require a lower front end. It's extremely hard to make any bike with an 8cm head tube. Here's where an integrated headset makes some sense. You can make this bike with 10cm of head tube, and because the bearings are now inside the head tube you save 2cm of stack. Voila, you can have your 700c-wheeled steep seat angled bike and get low enough without having to resort to a stem with extensive drop.
The same principle applies for those who need something shorter than a 47cm bike in 650c. Again, you can't go below 10cm or 9cm of head tube height, and if you need to get the bars lower in front an integrated headset will buy you an extra 2cm of "lowness."
For this reason, I think for bikes built on the margins - 650c tri bikes below 47cm or 49cm and 700c tri bikes below 55cm, or 700 road race bikes below 50cm for that matter - integrated headsets make sense.
What ought you to watch out for?
Good bike makers have always reamed their head tubes after the bike was welded. This is because welding a bike may tend to very slightly distort the tubes. So, if you did your cutting - if you cut the BB threads, reamed the head tube, stuff like that - after welding instead of before, your cuts were more true. The alternative to this is to do your cutting and threading prior to welding, but to at least chase the threads and re-ream the head tube (usually with lighter, hand-held tools) after welding and heat treating the frame.
I mention this because with an integrated head tube the reaming and chamfering must be more exact. It's a more complicated process, there are angular cuts that must be made, and it is perhaps more requisite to do your head tube cutting after the frame is made versus before. This is always tougher to do, because it's a lot harder to fixture a frame in your mill or lathe than it is to fixture just a round tube. Therefore, I'll make the general statement that one might theoretically be better off not employing integrated headsets in bikes of a lower quality. While I might like an integrated headset in my Cervelo - where I know the cutting is done post-welding - I might not want an integrated headset in a $600 road bike, unless I check in advance whether the headset was done right.
What do you give up with an integrated headset? It depends on who you talk to. First I guess I'll cause a bit of grousing by those who disagree with me by pointing out what you don't get: your integrated-headset bike won't be stronger and the steering won't be in any way better. It probably won't be worse, but it won't be better either.
Otherwise, realize that the head tube using an integrated headset is fatter, since you've got to stick the bearings inside, instead of above and below. If you're using a 1" fork with a standard headset your steel bike's head tube is going to be 33mm in diameter. In an aluminum bike it'll be 35mm. If your aluminum bike has a 1 1/8" fork the head tube's going to be 38mm or 40mm in diameter. Make that bike with an integrated headset and your head tube is now 45mm or 46mm in diameter. If you're looking for every aero advantage this will be a consideration.
The second issue is only one which a former bike manufacturer can appreciate. For the last several years of owning and running Quintana Roo I had my builders use head tubes that had a lot of wall at the top and bottom (in the case of steel bikes I had a ring sweated on the top and bottom of the head tubes). Why? Omitting for the purpose of this discussion issues of burst pressure and fatigue strength (in aluminum tubes), there was the very simple reality that in shipping, or while in the retail shop, it was very easy to ding the front of the head tube. It's a very vulnerable spot. If there wasn't a headset already in the bike, forget trying to press one in after you dinged it. With an integrated headset the situation is even worse. The bearing has to fit in there perfectly. If you ding the tube and deform the area where the bearing goes you're pretty much screwed. I'd be quite scared, as a manufacturer, to send a bare frame out if it was built to take an integrated headset. I'd only send out complete bikes.
Keep in mind that not all integrated headsets mean that you get that 2cm reduction in stack. In the case of Litespeed, for example, you can't easily machine a head tube in titanium that accepts bearings the way you can machine aluminum. Without going into detail as to how they do it, one will notice that Litespeed's bikes are made with head tubes that extend above and below the top and down tubes, and bulge out in the bearing area. If you can imagine an aluminum bike with headset cups welded into the head tube, and with the whole frame painted to appear as if it was all one integrated unit, that is what the Litespeed-made integrated-headset ti bikes will resemble. In such bikes there is no stack reduction though the bikes have integrated headsets, and this includes the Blade, the Saber, and QR's Tiphoon. Also, the head tubes on these titanium bikes, it must be pointed out, are not any larger in diameter than on bikes with traditional headsets.