Analog vs Digital Guitar Pedals: What's the Difference?
Digital vs Analog
The easiest way to point out the difference between the analog and digital signal is to look at the graphic representations of both. The analog signal is represented with a continuous smooth line. The digital, on the other hand, would be represented with a line resembling stairs going up and down. In the digital signal, each individual dot is equally spaced from one another.
We can (sort of) put it like this: the analog signal has "infinite" resolution while the digital is dividing the analog signal into bits. The quality of the digital signal can be defined by resolution. For instance, the music of those vintage video games is in 8-bit resolution. The standard audio CD has the resolution of 16 bits.
However, although digital signal can't have enough bits to replicate analog, it's difficult to hear the difference between the two at higher digital resolutions. Unless you have trained ears and very, very expensive equipment.
So what about the guitar pedals?
The analog pedals have the continuous "smooth" signal while with the digital pedals it is made of individual "points" and has a certain resolution. In digital pedals, the signal first passes through an analog to digital converter (or A/D) which "translates" the analog signal from your guitar to series of 1s and 0s. The signal then goes through certain algorithms and then goes into the digital to analog converter (or D/A) and goes out of the pedal as an audio output.
Obviously, there is some information loss when going through the digital effects pedals. But at the same time, if the audio resolution is high enough, there's a chance you won't really hear the difference. Of course, if the audio resolution of the pedal is higher, there's a chance that it will cost more.
What should I buy?
With the analog pedal having continuous signal passing through its circuits, the tone should be more "organic" and warmer. The initial thought here is that the analog pedals are better. However, there is hardly any point in getting an analog pedal if your amp features digital processing, as this resolution will be lost.
There are certain advantages and disadvantages to both. For instance, digital effects have more consistency as the sound will be processed the same every single time. The analog pedal, however, will allow you to reproduce certain nuances of your playing, which may differ from performance to performance. Instead of going through algorithms, the signal in analog pedals goes through capacitors, resistors, and transistors, and sometimes even tubes. This might provide you with more dynamic response compared to standard digital effects. It's usually the vintage lovers that enjoy this kind of sound and dynamic response.
But in the end, it all depends on what the player wants and the best option would be to try something out before you buy it. Also, the digital effects are now getting pretty close to analog pedals where you aren't able to recognize the difference if the bit depth and the sampling frequency are high enough.
There are numerous products out there to explore. But if you're looking for some popular analog distortion or overdrive pedals, you might want to check out the Electro-Harmonix Big Muff Pi, Ibanez TS9 Tube Screamer, or Fulltone OCD.
As for the digital pedals, there are countless multi-effects pedals or modeling amps where the sound is getting pretty close to the original analog effects and amps. Even some not so expensive products like the Boss GT-100 might even do the trick. And in case you need more versatile and realistic stuff, maybe try out Kemper or AxeFX. These are, however, often pretty expensive but are slowly replacing entire live rigs with many famous guitar players starting to use them for both live shows and studio sessions.