How do I compare weapons in-game?

Is there a way to compare statistics between two weapons in the game? (for example in Destiny by holding the R2 button I can see in green what improves and in red what get worse between my currently equipped gear and the one I'm gonna to buy)

Yes; as long as you own one of the weapons you want to compare, and have access to the other by owning or being able to preview it.

In the Arsenal (the place you equip weapons), when you enter the Equip screen you can select a weapon other than the one you're using and the stats will be shown in the stats screen on the bottom right, in comparison to the weapon you're holding. Green values are improved, red ones are decreased.

This compares the base stats of the weapons, before any mods are equipped, as the mod effects will almost always be proportionally the same on both.

The only weapons you can compare this way are the ones that you personally own, or the ones that are available to buy through Platinum. This includes all basic weapons, but excludes all Prime and Syndicate weapons.