I have to admit to a particular liking for Vienna regulators, partly because they beat slowly but don't take up anything like as much space as a longcase. Sometimes, the term "Vienna regulator" is applied to German spring-driven wall clocks of a similar appearance but usually smaller size. Those are affectionately known as 'Springers' and I comment on those separately under wall clocks.
A real Vienna is always weight-driven because unlike a spring, a weight provides a consistent power source. Commonly, they strike the hours and half hours on a gong (a coiled spring) attached to the cradle in the case. A service costs £175 for a striker. Less common, but quite charming, are the timepieces - clocks that do not strike or chime so have what is called a single train, easily recognised as there's just one winding hole in the dial. These cost £125 to service if the existing gut line can be re-used. The rarer and more valuable Viennas have three trains and so chime as well as strike. Naturally they have three winding holes and three weights of course, sometimes engraved. Servicing these will be more expensive from £225. Broken gut lines can be replaced for £85 plus £20 per train. Bronze lines cost quite a bit more.
All paid for work's guaranteed for a year.
The Vienna almost always has a large brass-faced pendulum bob hanging on a wooden shaft. Wood is much less susceptible to heat expansion and contraction so it remains a consistent length and timing is improved. The pendulum hangs inside the case rather than directly on the movement - the movement simply links to it when slid or hooked onto its cradle.
They have a deadbeat escapement, which gives better accuracy as the 'scape wheel is not forced to recoil slightly with each beat of the pendulum, as happens with the more common anchor escapement. Most have Harrison-designed maintaining power to keep the clock powered during winding.
Nearly all Viennas run for eight days on one wind, using a small cranked key. A curious thing is the subsidiary 'seconds' dial which is marked for 60 seconds but in most cases only takes 45 seconds for the hand to complete one revolution. This is because, unlike a longcase clock which has a 'seconds' pendulum, the pendulum in a Vienna is shorter and swings every 0.75 seconds.
Oddly, the majority of Viennas were not made in Austria but in Germany although the Becker factory, one of the most prolific manufacturers, was in Silesia, which is now in the Czech Republic.
The German Springer, mentioned above, is a different animal altogether. It generally has a gridiron pendulum constructed of different metals to address the expansion problem. But being spring-driven and built using pressed out wheels, lantern pinions and bent strip pallets, it offers nothing like the accuracy of the weight-driven Vienna. However, they're less than half the price and look nice so you buy what you can afford.