All of these have different cons and pros tbh.
Mobile gaming, when I think of these its usually just games on my phone that have 5 minute rounds, or I'll play for 10 minutes at a time. Its similar to handheld gaming, but its meant to be quick, and light (and usually free!). Many mobile games usually don't focus on the storyline aspect, but the gameplay. Whereas handheld games keep the portability, but when I want to play a 3ds game, I get invested in the story and the game takes focus and time to complete. Mobile gaming for me is usually just for quick and simple entertainment.
Console gaming is pretty easy to get into, you get the console and game, and its all set up for you. This is really the main type of gaming I've been involved in. Mainly for the Nintendo exclusives, looking forward to the newest games is usually what I've done, so I've never invested time into PC gaming.
I can't say much about PC gaming since I don't do much it (although one day I'd like to). PC gaming seems to be a little more complicated, especially if you're going for something specific. This can be both a con and pro, much more customization then the other categories. If you're decently serious about PC gaming, this can be great for many people, but confusing or slightly intimidating to newcomers. PC gaming can also usually be slightly more expensive, but seems worth it. PC gaming has usually given you a larger choice of games and more exposure to indie games (but consoles are getting better at this now).
Ultimately each version is different, and good in multiple ways.