Shadow Gun Legends is probably the closest it comes to console gaming. Although it almost feels like a destiny re-skin but with its own charm and mechanics to separate it. 
It puts players in a world where Fame, money, and being on top of the leader board is 5op priority, as you will tell with the many leaderboards everywhere. And the giant statue i. The middle of the hub world that displays the world's current "best" player which is determined by the amount of Fame you have. 
It can honestly be a good motivation tool if you like bragging rights.

* The graphics are great for mobile, especially with a phone that handles max settings.
*It is a free game with online purchases amd micro transactions, most micro transactions are easy to completely bypass there these lootbox like boxes the you can collect/earn, all which require keys to unlock. So far I don't believe there is a way to acquire the keys without paying for them which is a let down due to these boxes take up valuable inventory space so unless you pay money and open them, they are wasted. 
But other than that most items can be bought with game currencies or earned. I never really felt like i was in a huge disadvantage while playing, and when I did it wasn't anything a few tweaks to my character weapons and skills wouldn't fix. Without spending real money!
*Controls for touch screen are pretty tight and responsive. I personally like bluetooth controllers but I honestly don't mind occasionally using the on screen controls. They will take a few minutes to get used to but onces you do it feels natural.
*The game has a story mode that while it isn't to ground breaking. Still provides some fun and is a great way to get some nice gear. 
There are some non game breaking down of the  story/campaign, story missions are locked behind the player level. Which means if you want to continue playing a mission but your not up ti the required level. You have to leave and grind some XP and level up a few levels before continuing. Although the game does let you play some missions that are one (1) l evel above your rank for some added challenge. Which is really fun!
* Online multiplayer is present in the way of WARGAMES this contains games modes like 1v1 duals, capture the flag, team duals and more. But again these online playlists are unlocked as you level up.this can be a good thing or bad thing depending on how ypu like to play. I myself like having all game modes unlocked and ready to go from the start. It gives the online multiplayer more variety to do. Especially when you need to grind for XP to unlock the next stort mission
*There is a skill/ability tree in the game which is nothing ground breaking or new but its there and works nicely. Nothing to complain there.
All in all I would say this is a solid game to pick up for your mobile device, especially since it's free! 
Just make sure your device can handle max settings for the best experience!