Democratic Gun Control - Remove the capability to purchase assault type weapons and multi capacity weapons from law abiding Americans restricting the 2nd Amendment to hunting guns and single shot weapons, if that.
Republican Gun Control - AIM Well and HIT what you are Aiming at!
Now with that said I will offer up an opinion regarding the intent of the 2nd Amendment. The 2nd Amendment was important enough that the founders made it second only to free speech and freedom of religion. The founders were intent on giving citizens and citizen militias weapons capable of allowing citizens to take over their Government from one that had been taken over and run contrary to what the Constitution stated. That means military type weapons or the same weapons as the Government itself would possess or have at it's means. So I believe that means military type weapons available to all legal, law abiding citizens covered by the 2nd amendment.
That said there are many things that the founders didn't foresee or couldn't have known such as weapons that were of the nature the one man could alone hold off many others or kill so many alone. Still if you go with the intent of allowing citizens and citizen militias of taking back a Government stolen and run amuck then you have to conclude that whatever the Government can possess then the Citizens should have the ability to possess and obtain. Background checks and some sanity in defining just who can obtain a weapon under the 2nd Amendment freedoms is rational and within the scope of what the founders would want but removing the ability to purchase certain type weapons and purchase ammunition I believe is not warranted.
Many liberals want to remove American's 2nd Amendment rights either through the courts, judicially, or legislatively or by executive order. Such a move, in my own opinion, would warrant just the insurrection and bring about just the citizen action that the 2nd Amendment was conceived for. Mind you that' my own opinion.