II - 'looks like shit. Even by oldschool standards'
Actually, I find that the biggest problem with TF II is the too-fast ship speed in the overhead stages and the must-memorize traps in the horizontal stages.
III - 'lots o'cheap deaths and bad controls'
I'll agree with the lots o' cheap deaths part to a point--meaning that there are sections that must be memorized or it's a trap leading to a guaranteed loss of a ship--but the controls are not bad at all. More to the point, movement controls respond instantly and there's no inertia when the controls are released (the one exception is the underwater level and the bubble currents are still easily negotiated with the accurate movement controls). One button auto rapid fires, another button changes weapons, a third button changes ship speeds. It's actually a rather well designed control system.
IV - 'moar cheap deaths and bad controls'
So having learned from II and III that memorization is a required part of the TF series, I'd expect that IV would require memorization. That said, IV actually has the least cheap deaths in the early stages--it saves those for anything stage 7 and later.
Controls are also not bad in IV, even if there is a very slight inertia to the controls whenever the screen pans up and down (examples include Stage 1/Strite, Stage 4/Daser, Stage 5, Stage 7 with its numerous branching points, Stage 8 with its choice of up/down branching), but it's just as responsive as in III but with an even finer ship speed control system. So then one button auto rapid fires, another button changes weapons, and the ship speed button--press/release the button changes the ship speed in 25% increments, while press/hold the button changes the ship speed in 1% increments.
Also note that the game allows weapon change and ship speed change while the game is paused (and that can be useful if a player finds weapon change or ship speed too difficult without pausing, but I can do that without problems). Another feature is that the game even allows two player partnership, one player can focus on just movement while the other one uses the other controller to fire and change weapons.