This will be two things: explaining the differences between the two for your understanding, and sharing my opinion in case you don’t know which one to go with. This debate is specifically for fretted instruments, if you play anything that doesn’t have frets, your only option is Standard Notation anyway.
Standard Notation
Every school I know teaches using standard notation exclusively. For most instruments, it’s the only way to write and read music for them. If you plan on getting into any school bands, you will need to know how to read SN for your instrument. Also most jazz and classical music is written in SN, although I’ve seen a lot of modern Tab or hybrid versions. Another benefit for learning SN is the aspect of reading rhythm. This is the big reason I think it’s beneficial to learn SN even if you don’t need it. Also, students that already know SN usually find it easier to start their new instrument with SN.
Tablature
Most modern music books use either only Tab or both SN and Tab. Modern meaning anything in the past 100 years or so. Tab is super easy to learn, students get it right away, it takes about 20 seconds to explain. You can instantly start reading music with this method. Most website and apps use Tab, and most of the user-submitted music on places like Ultimate Guitar are written in Tab. This is important if you plan on learning music from more obscure artists that probably won’t have songbooks or anything like that.
Choosing one over the other
Like I said, if you’re doing anything in your school band you need to learn SN, so that’s an easy choice. If that’s you, and you also want to learn other modern music, then you’ll need to learn Tab as well. Which is easy. On the other hand, if you’re not doing music in school or studying classical music or jazz, you don’t need SN. I always recommend learning the basics of SN though, even if it’s later on in your journey after you build some skill. If you just want to learn for fun, and you’re not serious (yet) about digging deep into music theory, then I would just start with Tab. I learned using Tab, and picked up SN after I was an advanced level on guitar. It was pretty easy actually.
Another big difference between the two is that Tab doesn’t have rhythm, it’s not a complete form of writing music(yet, see below). You’d have to know what the song sounds like, which isn’t a problem in most cases, but it’s worth noting. On the other hand, with SN it’s kind of messy notating things like which string a note should be played on, whereas with Tab it’s already there in the format. Not a huge deal but it can get messy. In order to sight read on guitar using SN, you might have to read 4 things at once(the note, rhythm, string, finger). I’ve spent so much time on classical guitar figuring out how to interpret certain passages.
Too long;Didn’t read
If you’re doing music in school, learn SN. If you’re learning music outside of school, especially just as a hobby, start with Tab and go from there. It doesn’t hurt to learn both eventually.
Bonus idea, there’s this sort of “hybrid tab” that Ultimate Guitar uses which I love. It’s basically regular tab, but each number note has a stem like SN. It’s the perfect answer to the issue of Tab not having rhythm notation, it makes Tab a complete notation language, and I hope it catches on and becomes more popular.

