There are two main styles of Arabic scripts used in the Quran today. Both are widely circulated and known by various names.
Firstly, we have the Uthmani or Madani script and the second is known as IndoPak or Farsi (Persian) script. Both employ the Uthmani script standards but differ slightly in the convention of the diacritical marks.
The two scripts are written by different calligraphers who have different writing styles. There are technical differences as well. The IndoPak script is usually found in the 13-line Qurans, which are more commonly used in the Indian subcontinent and South African regions. The Uthamni script is usually found in the 15-line Qurans and is more commonly used in Arab regions.
The IndoPak script has been simplified so that learners do not need to know essential Arabic grammar rules such as having to differentiate between the letters Alif or Hamza, mute letters, it has a simplified method for writing alif/hamza, long vowel letters, Huroofe-Maddah, Alif Maqsurah or Khari-zaber, Madd-e-asli, Maddah ya or Khari-zer and Maddah waw or Ulti-pesh and some other minor variations. Furthermore, the IndoPak Qurans are divided into sections known as Ruku, these are not found in the Uthamni script Qurans. It also employs more pause/stop signs (Rumiz al-Awqaf) than the Uthmani version. Both produce the same results in terms of final pronunciation. However, each one uses a slightly different system.
Many people tend to read what they are comfortable with, a lot of it depends on your Quran teacher or parents (which version they were taught). Personally, we grew up learning from the IndoPak script so it came more naturally to us. If there’s one thing I could say that is a benefit of the IndoPak script, it’s that Tajweed wise it is far more ‘idiot-proof’. You say what you read (assuming that you understand basic Tajweed rules like idghaam). The IndoPak script also has many more notations for where to stop, when to continue, when to take extreme care in pronunciation, etc. This, once again, is because it’s assumed that the reader doesn’t know. As far as the drawbacks of the IndoPak script, there are a few such as the dreaded way that the calligraphers will conjoin 4 characters all in a jumble, and you have to decipher what’s going on. Also, the vast majority of IndoPak Qurans don’t end the ayah at the end of the page, so you may be caught mid-ayah when you’re turning.
If you are comfortable with Arabic, then the Uthmani Script is the better format. I like that each page ends the ayah (which is good for memorising) and that each juz is 20 pages (good for pacing). There also are no letters that are jumbled up making it much cleaner and neater of the two scripts. If you don’t know Arabic that well, then you may have some trouble with the Uthmani script.
There are lots of Hamzahs that are not pronounced because they are only there for enabling purposes when you restart from a pause. Or they may be there to show a verb is plural (usually coming after a waw) and are silent as well. They assume you know Arabic grammar, so when to pronounce the enabling Hamzah with a kasrah or dhamma in a command. Also, you will see fewer marks indicating stopping points, because the assumption is that it makes sense to you when you are stopping.