No one, no matter their circumstances of birth, is going to argue that Tywin was an admirable, perfectly just or good lord. He made enemies of everyone and ruled through fear.
He's a man who was born into privilege and power, saw that he could have more of both if it were not for the fact that many of his peers envied or eyeballed what the Lannisters had with greed, but instead of trying to turn those desires against them and try to use it to better the land he ruled, he decided to remind people "oh yeah, Lannisters have all that stuff and can use it to crush anyone who dared to desire it in turn".
When he rewarded people for doing what they wanted, that was at best maintaining the status quo. It didn't get people to exercise better judgement, it just fed into the negativity that already existed (greed) and punished the other (envy) when they went against him in any fashion.
Tywin was never satisfied if he wasn't on top. Even while being Hand, he took it as a
natural expectation that while he may not be King, his grandchildren would be, and wouldn't forgive Aerys for not acceding to that despite being his "strongest supporter", or rather the person that took advantage of circumstances and childhood friendship to make certain at best Aerys would be
called King but wouldn't ever get any of his projects off the ground because they weren't moderate enough for his tastes, which was why he turned back Aegon's reforms.
Aerys probably didn't give a shit about the reforms even on his sanest days, but one can't help but think the fact that Tywin pretty much ensured a generation of Westeros didn't remember one single thing relating to having power over an entire continent could be attributed to House Targaryen directly, aside from which Houses benefited from close ties. Which admittedly would have been enough, since before the rebellion, most people were willing to stomach Aerys' court so long as the heir on what seemed like a much more even keel would eventually take over. Hopefully saddled with "the right bride" with "the right blood", when to Aerys' mind, they are dragons and no one should be "as worthy" or dare I say, "more than worthy".
None of these things speak well of Aerys, but it was Tywin's job to advise him and part of that would be getting him to act at the head of charge of any actions the Crown took, so that the King didn't look weak or like a puppet--if that was in fact not what he wanted.
I mean this is the least of what we can condemn about Tywin's part to play, that's just the dynastic drama he failed to properly manage, he also failed to make anything of his tenure as ruler of Westeros besides making the Crown wealthy, nothing of which was actually used to improve the realm (because Tywin didn't want anyone else to benefit from the eventuality of rule, and to make his grandchildren look like good Kings they would have needed that nest egg for any reforms
he impressed them to impose). in ASWaH
@DragonParadox stated that Tywin wanted to centralize things a good deal, and we can guess he might have aspired to do the same in canon had the WoFK not occurred, but having Aerys get credit for any changes wouldn't have been ideal for him (seeing as how he spited his former friend's treatment of him despite taking advantage of that friendship to benefit his own legacy).
TL;DR - These are both bad men, but Tywin's the one alive and in front of us, so we can only punish one of them.