Preamps generate more discussion per unit of audible effect than almost anything else in a studio. This is not because they do nothing. It is because what they do is small compared to what is sitting in front of them, and the order in which people spend money rarely reflects that.
What a preamp actually does
Its job is to take a microphone-level signal and raise it to line level with as much of the original and as little added noise as possible. Designs differ in how they colour that process: input and output transformers add saturation and shift the frequency response slightly, discrete circuits behave differently at their limits than integrated ones, and some designs deliberately distort in a way people find pleasant.
These differences are audible. On a solo source, in a quiet room, with good monitoring, most engineers can hear them. The question is not whether the difference exists but how large it is relative to the other differences available.
The order of magnitude problem
Consider what changes the recorded sound of a vocal, roughly in descending order: the singer, the performance, the room, the microphone choice, the microphone position, the distance from the microphone, the pop filter, and then the preamp. Moving a vocalist fifteen centimetres closer changes the low end more than swapping between two well-made preamps. Changing the room changes everything.
None of this makes preamps irrelevant. It makes them a refinement applied after the large decisions are correct. Applied before, they are an expensive way to record the same problem more accurately.
Where preamps genuinely earn their keep
Three cases are worth the attention.
Gain range with quiet microphones. Ribbon and low-output dynamic microphones need a lot of clean gain. A preamp that runs out of headroom, or that gets noisy at the top of its range, will audibly degrade those sources. Here the specification matters directly, and a preamp with plenty of quiet gain is not a luxury.
Deliberate colour. Some preamps are chosen precisely because they distort. Driving a transformer-coupled input hard on a snare or a bass guitar is a real production technique, and it commits a sound in a way that a plugin applied later approximates rather than reproduces. That is a legitimate reason to own a particular box.
Impedance interaction. Some microphones, particularly ribbons and older dynamics, change character noticeably depending on the input impedance they see. A preamp with a variable impedance control turns that into an adjustable parameter. This is a small effect on most sources and a surprisingly large one on a few.
The listening test that settles it
If you want to know how much your preamps matter on your sources, run the comparison honestly. Record the same performer, the same part, through two preamps, at matched output level, and listen without knowing which is which. Level matching is the whole experiment. Without it, the louder one wins, every time, regardless of quality — this is one of the most reliably documented effects in audio, and it does not stop applying to people who know about it.
Most people running this test discover the difference is real, consistent, and smaller than they expected. That is useful information, not a disappointment. It tells you where the next improvement should come from.
What to buy first instead
If the budget is finite, the sequence that produces the most audible improvement per unit spent is usually: treat the room, then improve monitoring so you can hear what you are doing, then buy a microphone appropriate to the source, then buy a preamp. Room treatment is the least exciting purchase on that list and reliably the most effective.
The corollary is that a modest interface preamp is not holding back most home recordings. Converter quality and preamp quality in current interfaces are good enough that they are rarely the limiting factor. The limiting factor is usually the room, the monitoring, or the performance.
A note on stacking
There is a tendency, once someone owns a good preamp, to route everything through it. Resist it slightly. A colourful preamp on every source produces a recording where everything has the same colour, and the character that seemed appealing on one track becomes a haze across the whole mix. Use the interesting one where it does something, and use the clean one everywhere else.