To my mind, the safest, most useful, and least likely to break are the Bachmann abd the French Prusiks. This is not to say that Klemmheist and Classic don't have their uses. It's just that the former have worked best for me and have a provable record of overall safety when using 5mil cordage. Furthermore, they are both easier to move on wet, icy or dirty ropes, where the latter two will seize solid under load and may have to be cut. As for general strength, they are pretty much all equally comparable with only a small variation of shock-load in favour of French and Bachmann. The one perceived disadvantage of a Bachmann is that it requires a Krab to complete its function.
The advantage is that the Krab makes a great Jumaring handle for cold or tired hands; you can get more turns on the rope with a larger Krab, and a simple outward lift on the Krab loosens even the wettest, most frozen Prusik cord. A lot of climbers seem to be obsessed about their Prusiks slipping on wet or icy ropes. Whatever Prusik you use, the answer is simple: just take a few extra turns round the ascent rope.
The main problem, as most experienced climbers will know, is when a Prusik jams or locks solid on the rope, and one has to prise or cut the bloody thing off! Either a well-tied Bachmann or French Prusik will settle this debate. One more tip is to always carry spare sets to replace worn or soaking wet ones. They can always be used as Abseil Anchor Ties on the way down, which saves loads of expensive Maillons or Krabs.
SOFT OR HARD PRUSIKS?... Sometimes a thicker, softer cord is far more useful than a thin, hard one. I won't dwell on it here, but suggest it's a good idea to get to know your local Arboreal Industry climbers. They have some great Prusik variations that you might find useful in varied Alpine conditions.
FIXED ROPE PRUSIK SYSTEM ... Not so long ago, there was a tragedy on the Eiger's Mittellegi Ridge where a rope of two climbers fell to their deaths whilst moving on a fixed rope. They were moving together along the fixed rope, connected by their alpine rope, but were not protected. One fell, dragging the other with him. If you carry a 2meter by 8mil Rope Sling as well as your Tape Slings it can be used as a protective Prusik on a thick Fixed Rope or Chain.
Simply rig a Bachmann Prusik of only a maximum of three turns around the rope, and clip it to the end of the rope sling. (The amount of turns is really dependent on the thickness of the fixed rope. You may require more or less.) This way even a rope of two can move Protected, and the same thing can be constructed using a bight of the climbing rope.
One final point on rigging Prusiks: keep them "looking tidy" as per the book! A tidy-looking Prusik will work well, and an untidy-looking one will not.