I personally prefer ballheads for speed and convenience. I had a cheap pan-and-tilt head once and struggled with it, and never got used to it, although many say its a matter of getting used to it. I've heard that pan-and-tilt heads are better for macro photography and the like, but since I almost never do that, life has become cheerier since the purchase of my ballhead.
If you do decide to go with a ballhead, do find one that is the appropriate size and weight for your equipment, particularly if you have heavy lenses. It's usually a compromise between ballhead weight (some weigh a tonne) and the weight of gear it can support. I use a Markins ballhead after reading rave reviews about it on the Nikonians website, and I certainly have nothing but good things to say about it. It is fully compatible with the Swiss-Arca system and its plates. Check out the Nikonians website for more extensive reviews on this ballhead, but I have no complaints! I used a cheaper Manfrotto 438RC ballhead before but got rid of it after I found it a little clumsy with vertical compositions.
It's one of those things that's a personal choice, and you really need to try them out for yourself.
I prefer three-way pan heads, because I like things to be square and straight and it's easier to do that when you can control the three rotation axes separately.
Ball heads, though, are more compact and quick to adjust, particularly for moving subjects. I have a small Linhof ballhead on my little travel tripod, which I use for my smaller rangefinder cameras or even my ultralight 4x5" Gowland.
After more than fifty years of trudging about with all kinds of equipment, I have yet to find the need for a ball-head tripod. Caveat: I don't do nature (or children on the loose) for which one might be preferable.
I have used both types and find the ballhead much more convenient. I first started using it when I was on staff at Outdoor Photographer magazine on the recommendation of one of the contributors. A good ballhead is fast and smooth and I can level mine faster then I can level a 3 handle model. I have a heavy duty Bogen (Manfrotto) and love it.
I have each for different sized cameras, The only extra thought I have, with the larger cameras, 5x7 and up it is easier with the 3 way because you can adjust one direction at a time. Personally I prefer the ball heads for speed and flexibility. You do need to keeep the ball lubricated though.
I had a pan head before, and I let myself be seduced by everyone recommending a ball head a year ago. My conclusion: I much prefer a pan head. I find it gives a more precise control, plus, you don't need a mega-bucks panhead for it to work well, while I'm not sure I would say the same about ballheads.
Sorry if this reply is late. I started out using a ball head with 35mm and medium format and they are indeed quick and easy to setup. I just wish I'd bought the bigger ball; the one with the friction control.
I now use a pan and tilt. No sudden changes of camera position = no sudden changes of center of gravity = no sudden contact between camera and ground !
FLM makes a ballhead which will not tilt sideways if an additional clamp is locked. Once tripod and camera are level and this clamp has been fixed adjusting the camera becomes more like working with a two-way pan-tilt head. All in all it is a nice head which replaced my Linhof Pro III.
Well, if you will do panning with your camera(following subject while it moves) it is easier to do with 3-way than ball head. You can, for example, have fixed vertical movement and have free only horizontal movement fot taking photo of moving car while follow its moving. With ball head you will have horizontal and vertical movements free at same time which can be problem if you need vertical or horizontal strictly fixed...
Some ball heads have a separate pan swivel with a lock lever at the bottom. I had one for a while but it annoyed me because I was always grabbing the wrong lever to adjust the thing. I sold it and got the simpler version.