This is the new title screen, where I've only made subtle changes, but I think it looks much nicer than the previous.
The new movement system is much smoother than the previous one that only allowed for 4 directions. The new system allows players to move diagonally. I figured this out by making the movement keys affect a 'velocity' variable instead of the x and y variables directly.
I also made it so bullets can collide with each other instead of just passing through, which gives players a method of defending themselves.
One of the issues I had with the game was not knowing how much health each player had, besides the sprite changing to an "injured" version when health got below 50. I added in healthbars for the player using this tutorial.
The biggest update I made was the addition of gamepad support. It makes for a much better experience than having both players crammed together on the keyboard. The only thing that didn't work correctly was using the right stick to make the ship turn. I implemented it, but it was far too finicky and sensitive, even with the deadzone set as high as Gamemaker will allow. For this, I used this excellent blog post.
Since the players can't turn, there is a potential problem with players getting on an even level horizontally which would make it impossible for them to shoot each other. To combat this, I added a 'black hole' across the middle of the screen that blocks the user from crossing it and also hurts them. It should make it so that players are always able to shoot at each other.
The only thing left for me to do is implement my own art for the player ships and bullets.