O.K. This is a big topic with guitarists. Guitarists generally seem to compose original music fairly easily. I've worked with a lot of music students and it seems like guitarists always write original music of some kind while that is rare with other instrumentalists for some reason. Maybe it's because the guitar is such a visual instrument in which you can sort of "see" all the notes right there on the fret board. But, and you guitarists know what I'm going to say here, guitarists resist reading music more than any other instrumentalists. This is probably because it's pretty natural to play the guitar by looking at it and finding the notes, or from using your ear to find the notes. The guitar is actually written in standard notation up an octave from where it actually sounds and the notes on the guitar can be found in many places. Once you change positions on the guitar, meaning you move your range of motion from open to 4th fret to being more based around the 5th or 7th fret, the position of all the notes changes. Believe me, I get it, standard notation can be difficult to ready for guitarists.
So, we generally are sort of afraid of reading music. Since reading is sort of rare for guitarists, writing music out for compositions also seems pretty rare. And, of course, tablature is lot easier to read than standard notation. I learned to read standard notation on the guitar and I did that pretty much exclusively for years. These days, I use tab almost exclusively. I feel a twinge of guilt or weirdness writing that even now. The guitar teachers I had very much looked down on reading tab and I get that, but I use tab all the time now. Sorry guys. I know that isn't allowed but oh well. Too late to change and you can't flunk me now!
If you compose music or if you come up arrangements of other songs, I think it's extremely useful to physically write out your music. I know what you're going to say, "I record my songs and I don't need notation." How many songs have you written? It gets pretty difficult, at least for me, after the number of pieces you've written grows. Also, I have a pretty good memory but I can't remember every song without notation, especially since I write in a lot of different tunings, another reason I use tab for writing out songs now.
I have had the terrible experience before of forgetting what chords or fingerings I used for a particular song. It's no fun to not be able to play your own songs. I also used the "I'll just record everything" method for years until I kept having that experience of forgetting how a piece was played. At this point, I physically write out all of my music and arrangements, if only so I can use it later to remember how I played the song. But, also, it's really useful for me to put the notes and fingerings down on paper so I can see what's going on in a composition or arrangement. I always use pencil and I erase all over the place. Usually the pages are pretty messy by the time I'm done and often the final piece has to be rewritten to make it even legible. When I studied music arranging in college, my main professor taught me that the paper should look really messy if you're really working on the composition. If you're really experimenting and trying different things out, you'll end up erasing and crossing things out and putting little arrows all over the pages. Make a mess. It doesn't have to be pretty. The arrangement is basically a tool. When I used to show my compositions to my teacher, he would say, "Why is the page so clean? At this point in a new composition, the pages should be messy with lots of eraser smudges on them. Bring it back next week but it better be messier." I didn't really understand what he was talking about at the time but I get it now. If you're really working on a piece, the pages will generally look messy.
A lot of people use GuitarPro or some other digital music notation program for this. I use GuitarPro for the final arrangement if I'm going to put it online for others to use, but I never use it to notate the songs while I'm writing them. Using a paper and pencil isn't very high tech. but it works better for me to do it the old fashioned way. I'm also thinking I'm going to stop using GuitarPro altogether. I get very frustrated with it and it takes me a long time to notate songs on it. It's sort of fun, but it sure is time consuming.
I'm also very aware that there are many guitarist composers who are much better than me who never write anything out. Their memories are either better than mine or they don't mind forgetting pieces or they don't mind going back to the recordings to try and figure out what they played. So, I'm sure a lot of people can write effectively without writing their pieces out, but I also know that I am not one of those people. I have a big filing cabinet in my music room filled with compositions and arrangements that I've written out. It's nice to be able to go back to these to relearn a piece I've forgotten how to play.
So, my free advice to guitarists who are starting to compose is to get your self a big stack of blank tablature paper, a whole bunch of mechanical pencils, a box of file folders, and some kind of filing system. Writing out the compositions long hand was good enough for Bach, Beethoven, and Mozart and it's good enough for me. Also, if you ever see pictures of Beethoven's hand written scores, they are very, very messy.