Comparing piano with guitar is like comparing buckets with spades because they both do different jobs. A piano is a bigger, more capable instrument but it has drawbacks. A guitar is more portable and easier to get along with, it's also better suited to certain styles of music like rock, folk or Latin.
1. A piano has greater tonal range, it can play higher and lower than a guitar. It can also have more than six notes sounding at the same time.
2. Because you can play notes with both hands, a piano gives you infinitely more options in terms of rhythm, texture and timbre. It also allows you to create richer more interesting music.
3. A greater range also allows you to compliment your vocal range much easier, this is especially important for male singers who's voices always conflict with the limited range of the guitar.
4. All the notes are laid out before you, so you can see what you're doing. This makes it easier to see the patterns, relationships and intervals of music which form the basis of music theory. This is much more important than you probably think it is.
6. A synthesizer gives access to thousands of sounds which are much harder and more costly to use with a guitar.
So purely from a musical perspective, the piano is bigger, better and a more useful instrument. But when compared to a guitar, it does have drawbacks.
It's harder to learn because when you learn piano, you are learning a lot more about the structure of music as well as the instrument. For example, because the notes are all laid out in front of you, you'll be adding bass accompaniments and rhythms quite early in your development.
Learning to sing whilst playing a piano is harder because your mind has more to cope with.
You'll also learn about upside down chords ( inversions ) and all the theoretical keys simply because they're really easy to see on a piano. They're also easier to play. Some keys are very hard to play on a guitar - which is why you either use a capo or you learn to avoid certain keys.
Ultimately, with piano, you'll be learning to create richer music, much sooner than you would with a guitar. This is definitely more difficult at first. But it's really important too because accomplished musicians find songwriting much easier.
There will always be times when you wish you didn't have pack up cables and amplifiers and a piano stool and a keyboard stand and a pedal. It's a real drag. Especially if you only have a bike. And extra specially if you have to make several journeys across a car park populated by a gang of idiots who keep calling you 'Mozart', or 'Elton' who then try to steal your gear.
Alternatively, an acoustic guitar goes in it's case and you're pretty much done. This really does make a difference because no matter how enthusiastic you are, being a musician is hard work and you don't want to put more hard work or hurdles in the way of you doing what you need to do.
Because your guitar is strapped to your body, it's easier to perform standing up. Performing and especially singing, is really difficult if you're sitting down. It's ok in the bedroom, but when you get in front of real human beings you have to be seen and you have to sing properly, you can't do either sitting down.
You can also move around. This is better for your audience and better for you. A performer who's constantly moving is much more interesting than one who's tied to a fixed object. And your music is gonna make you want to move your body. It's what music does, doesn't it ?
With a guitar you're free to explore the whole experience with your body and being in front of an audience will encourage you to do that. But you can't do it with a keyboard, even if you're standing upright.
Even in the bedroom, when you're songwriting, it helps to be able to move around and get the feel of something into your legs.
Folk, Blues, Latin, Rock. The list is endless. No matter how much you try, some music just won't work well on a piano. A lot of it is due to people's expectations of which instruments should be used for a particular genre, but that goes with the territory.
If it sounds like it should be played on a guitar, then it should be played on guitar. If it's got a big rhythm element, it should almost certainly be played on a guitar.
With a guitar, you'll always feel much closer to the music and it's emotions than you will with a piano. This because you're touching the vibrating strings with your fingers and holding the instrument in your arms.
It's almost like you're touching vibrating heart strings and holding the music in your arms. It's not to be under estimated as it's a very intimate experience.
As a songwriter, you should make the piano your first choice instrument every time because technically and musically, a piano is far superior to a guitar.
A guitar has several advantages that a piano cannot match. Especially, when it comes to ease of learning, transport, performance and emotional connection to the music.
Best advice is to learn piano but also buy a cheap nylon string guitar. Because, once you've learned piano, playing guitar will be easy and writing songs will be easy. Doing it the other way round is hard.