The common misconception about bassoon sections is that the first bassoonist is always the stronger of the two, able to play with virtuosity in all registers, while the second is usually a backup, the lesser of the two. In reality, the second bassoon part is sometimes harder, and usually more important than the first part! In certain situations, seating a player who may be technically the best but have the strongest low range is often a better decision than seating a player who can't play low notes with precision consistently in the second position. Section chords, Tenor v. Bass, unisons, and octaves are all treated with different roles. I'll give a few examples to help explain this concept.
Unison. In Tchaikovsky's Symphony No. 6, mvt. 4, the movement opens with a long, slow (and tiring!) bassoon soli. The solo ranges from a high B to a low C, from fortissimo to pianissimo. It's an excerpt often asked on auditions, for good reason. The concept of playing in unison is a pretty simple role. The first bassoon leads in tone, intonation, rhythm, and dynamics, and the second player should follow the first in all these aspects.
Octaves. In Hindemith's March from Symphonic Metamorphosis for wind band, the bassoon parts are some of the most fun to play in the repertoire. The piece calls for two bassoons and contrabassoon, and usually the first and contra are in octaves, while the second bassoon is in fifths or the octave between the first and contra. Here it's important to always listen to the lowest voice for intonation. The first bassoon is least important when playing in octaves, so it's always important to adjust to what is given to you. A good contra player will lay down those bass notes so solid that the first bassoon won't even have to try to adjust.
Tenor v. Bass. Any baroque orchestral piece (let's say a Bach oratorio) will have your typical second bassoon bass line doubling the celli or string basses, but often the first bassoon will be playing the tenor line with the violas or violins, if there are two parts. It's important in this situation to think of the parts as equal in the section, but separate as an orchestra. The parts usually do not differ in importance, instead the roles of the bass and tenor lines in the context of a cantata both need to be heard. At some points the tenor line will need to be more prominent, other times the bass, but it's up to the performer to determine when those moments are. Typically the moving notes are most important, and when the long notes come, lay back a bit for the other parts to be heard.
Section chords. Ravel's Rhapsodie Espagnole, mvt. IV. Feria is extremely technically challenging for all instruments. It's a fun piece to listen to. Typical of most french impressionist music, the piece is more about color and gesture than precision and sound. Rhapsodie Espagnole calls for three bassoons, usually in chords (root, third, and fifth) no matter how fast the notes on the page, and contrabassoon, usually playing specifically with the tubas on downbeats and chords. When playing in chords in the bassoon section, it's important to first figure out if the bass line is present. If so, follow the bass line for not only a solid downbeat to bounce off of (most of this piece is conducted in one, subdivided in 3 with constant 16th notes), but also for intonation. If a bass line is not clearly present, the first bassoon is the most important if they have the melody or end on the tonic, but again it's up to the section to determine which bassoon is most important at any given point, as the tonic of the key or the root of any given might be present in another voice. Bottom line for rhythm, musicality and breathing is to follow the first player.
Adding the section to the ensemble. In more modern compositions, you'll find bassoons are usually doubled, often given the same part as trombones or euphoniums, but in any large ensemble composition through the first half of the 20th century, bassoons have a unique role. I find myself playing with clarinets, tubas, french horns, saxophones, trumpets, you name a section and I've played with them at some point. This makes the role of the section even more challenging as we add the component of blending with other instrument sections, which is just as important as blending as our own section. Playing more reedy and bright on the tip of the reed with the upper woodwinds, playing low and full in the middle of the reed and a slight delay in sound with the low brass, and right in the middle round timbre with a soft tongue for playing with the french horns. A great conductor will tell the group who should be the predominant voice in any piece, but sometimes it's up to the players to determine whether the bassoons should bring their part out, or blend with another section, simply adding color and strength. For example, in any Beethoven piece (ex. Beethoven Symphony No. 5 mvt. 3), any low cello soli is usually doubled by at least the second bassoon, if not both. The bassoon here adds color, but also adds a bit of definition to the cello section sound. This type of scoring calls for the bassoon to bring their part out a bit, but still stay within the sound of the celli. Usually in recordings you can barely hear the bassoon, but if it weren't there, you would notice!
Bottom line, playing as a section takes the skill to listen to each voice and determine which should lead and which should follow, while playing with the ensemble takes the skill to change the style of tonguing, length, timbre, placement, and dynamic to match any voice for an optimal performance. With the proper concentration, the bassoons can be the most versatile and interesting section in the group!
For more reading, check out Second Bassoon: Specialist, Support, Teamwork by Dick Hanemaayer from The Double Reed. (first page and "psychology" section" on p. 8)