Two basset horn designs are available:  the small bore (15.6mm) model, played with a Bb/A clarinet mouthpiece; and the medium bore (16.9mm) model, using a dedicated mouthpiece. 

For further explanation of basset horn bore sizes, please see below.

Unique features include a downward-pointing clarinet-style bell (for stronger bottom notes), and an angled, solid-body barrel (instead of a metal neck). 

Keywork normally includes plateau keys except for two open finger holes (L3 and R3).  An articulated C#/G# key is optional.  All models include an automatic register/throat Bb mechanism, for accurate twelfths and a clear Bb.

The standard basset key arrangement has low Eb played by the right hand little finger and three right thumb keys giving D, C#, and C, with the touchpieces shaped to allow smooth transitions between notes.  A low D key for the left or right hand little finger, in addition to or instead of the thumb key, is possible.  An alternate Ab/Eb for the left hand is standard. 

(For thoughts on the basset key arrangement, please see the article on the subject on this website.)

A choice of support mechanisms is offered:  a floor peg, or an abdomen brace and neck strap/chest harness, which allows the instrument to be played either sitting or standing with equal ease.

- The small bore basset horn has a bore diameter in the range of 15.5 to 16.0mm (still somewhat larger than a soprano clarinet bore, though it is often erroneously thought to be the same).  It is played with a Bb/A clarinet mouthpiece (or at least one based on the same blank).  Among other manufacturers, only Selmer makes this model.
 

- The medium bore basset horn has a bore diameter in the region of 17.0mm.  This is the most common type made by German manufacturers.  Since no French-style mouthpiece with an appropriate bore is mass produced, this model traditionally requires a German basset horn mouthpiece. 

(This model unfortunately is not usually recognized in North America, where it is incorrectly confused with the large bore type, below.)
 

- The large bore basset horn, with a bore diameter of about 18.0mm and played with an alto clarinet mouthpiece, is simply an alto clarinet pitched in F and with the extra basset notes.  The Leblanc and Buffet basset horns are of this type.
 

It is a matter of academic interest only which model(s) are recognized as "true basset horns" and which as imposters (though far too much argument is wasted on this question!).

An objective choice of the most appropriate model is based largely on the player's comfort with an instrument's required mouthpiece/reed, blowing resistance, tone control and articulation (besides, of course, availability).

It is unlikely that the majority of listeners would be able to detect much if any difference in tone quality among the various models of basset horn, when played by musicians of sufficient proficiency.