The biggest difference comparing one card to another is probably in the external analog circuitry. That is, what's not in the DSP chip.
The biggest difference between sound cards is mostly related to the clip level, which is determined by power supply voltage.
Regardless, the computer's volume controls should usually be set to “0 db” for best performance. In many cases, this is all the way up, but not always. Setting it to higher than 0 db will result in analog clipping. It may be tempting to turn up the computer's volume control to higher than 0 db especially on the cheap sound cards, but don't do it because it will sound bad.
For consumer sound cards, the connections are “unbalanced”, usually with 3.5mm TRS connectors.
The cheapest cards may not have any external analog at all. It just goes in and out with no external buffer. It probably runs on a single 5 volt power supply.
One step up is to have a buffer amplifier. Still, it probably uses a single 5 volt power supply. This limits the voltage swing to about 3 volts peak-to-peak, about 2 volts less than the supply. This corresponds to a sine wave of about 1 volt RMS, or “0 dBV”, or about ”+2 dBu”. This is about 18 dB lower than a typical high quality console (+24 dBu), a level that is considered to be “professional”.
Using a reference of an old-style analog VU meter, a good quality console would set the reference 20 dB below that, or ”+4 dBu”. Based on this analog VU meter, typical CDs usually set their reference between 12 and 20 dB below “full scale”. Let's pick -15 as a reference. The cheap sound card “reference level” is then -15 dBv, or -13 dBu.
This is typical of the basic motherboard sound systems and the cheapest sound cards. It's also typical of the USB sound cards, because the power for USB is 5 volts. You can get by if you must. Aside from the low level, they are really not that bad.
A step up from this would be to use the +12 volt supply for the output stage. This is capable of about 10 volts peak-to-peak, about 10 dB better than what you can get from a +5 volt supply. The clip level is now +10 dBV or +12 dBu. Using a 15 dB margin, that allows a calibration level of -5 dBV or -3 dBu. Using a 20 dB margin, that allows a calibration level of -10 dBV, or -8 dBu.
This is typical today's consumer audio equipment, such as CD players and the better mass-market consumer sound cards selling for less than $100. Some of the cards have an extra power cable, using the plug that used to be used for the floppy disk. In most cases, it's the level I recommend as the best cost/performance tradeoff.
A further improvement is to double that, often by adding a -12 volt supply for a total of 24 volts, or to use a single 24 volt supply. This gives you 22 volts peak-to-peak, a little more than 6 dB better, clipping at +16 dBV or +18 dBu. Using a 15 dB margin, that allows a calibration level of +1 dBV or +3 dBu. Using a 20 dB margin, that allows a calibration level of -4 dBV, or -2 dBu.
This is the level expected in “audiophile” equipment, including the better CD players. You don't find it in computers. The PCIE bus doesn't have negative power.
Going up to +/- 15 volts adds 2 or 3 dB. That's about all you can do unbalanced. Computers don't have 15 volts, but stand-alone boxes and consoles do. This is the common level and topology that most consoles use internally.
The best professional cards have balanced outputs. This gives you twice the voltage, allowing a calibration level (using 20 dB headroom) of +4 dBu, a level expected for professional equipment, when using a +/- 12V power supply. These are the best, but also the most expensive.
Unfortunately very few of the “balanced” cards can do this kind of level. Most of the “balanced” cards still use a single supply, which might be 12 or even 5 volts. The clip point would be twice what you could get with unbalanced. With a 12 volt supply (PCI card, not USB), the clip point is more like the +/- 12V unbalanced cards, +18 dBu clip, -2 dBu nominal. This kind would rank as second best.
With a 5 volt supply, the balanced clip point would be around +8 dbu, maybe +10 dbu. Opinions vary on whether this is preferable over the 12 volt unbalanced cards or not. It's only an advantage when it feeds a balanced load. My opinion is that in most cases the 12 volt unbalanced is preferable, because it can feed either balanced or unbalanced loads without losing headroom or level. On the other hand, a USB card can do this without a separate power supply.
Balanced outputs are a mixed bag. Some balanced outputs are “floating”, some are “non-floating”. To determine what is best, you really need to know what kind it is, and what it feeds.
Balanced INPUT is more important.
The record side of the sound card is subject to the same headroom issues as playback, but it is more critical because a source can overdrive the input stage leading to distortion that cannot be corrected by turning down the computer's gain control.
Again, the computer's volume controls, “capture” and the control for the line input, should usually be set to “0 db” for best performance. In many cases, this is all the way up, but not always. Sometimes the “0 db” setting is all the way down. Sometimes in this case, some programs, like Audacity, confuse the capture's “0 db” setting when it is all the way down with “off”, and it mutes. In this case, set “capture” for a little bit of gain, but leave “line in” at 0 db.
Setting “line in” to lower than 0 db will result in analog clipping ahead of the volume control. It may be tempting to turn down the computer's volume control to lower than 0 db, but don't do it because it will sound bad. If the record level is too high, you need to reduce the level going in. You can do this with a distribution amp, by turning down the source level, or with a resistor voltage divider.
Now, let's look at the input circuits you might find.
The cheapest sound cards use a simple unbalanced input that clips if the peak-to-peak voltage exceeds the power supply. That's fine if it is being driven by another cheap sound card or consumer device. A step up from that would use a different configuration, a higher voltage supply, or an attenuator on the input so it can take a higher input level. If you are feeding it from any “pro” source, you will probably need to cut down the level with an external “pad”. You can be sure the input is unbalanced if it has RCA connectors or a single stereo TRS connector with left and right on the same connector.
You need to be careful if you are feeding an unbalanced input from a balanced source, especially if the source is the “non-floating” type.
A better choice would be a balanced or differential input. Even if the outputs are unbalanced, a balanced input is always preferable. You can ground either side of a balanced input, with the only consequence being that it isn't really balanced any more. It is still better than an unbalanced input because it breaks ground loops.
Balanced inputs usually will accept a higher level, but you need to check to see what it really will take. Some of them still have less headroom than a professional grade mixer would have on its output.