Although it's a common joke among avid movie fans, there's very little in-universe evidence to support the notion that Imperial Stormtroopers are as poorly trained or inaccurate as you suggest.
This question addresses it well: Are all Stormtroopers as poor soldiers as the ones in the movies?
Add in other facts such as Obi-Wan Kenobi directly referring to the solid reputation of Stormtroopers, saying:
And these blast points, too accurate for Sandpeople. Only Imperial stormtroopers are so precise.
And upon closer inspection, the Millennium Falcon was likely allowed to leave the Death Star so they could be followed to the hidden Rebel base, rather than the assumed ineptitude of the Stormtroopers failing to prevent an escape and you quickly realize that there isn't much evidence to support your claim.
As for how they compare to First Order troopers, I don't know of any source that directly addresses any drastic steps forward or backward in terms of accuracy or training.
Episode VII does more to get the viewer to respect their troopers, though, creating the perception that they're more effective. The viewer is allowed to see some of the carnage up close and personal, for example, when they slaughter the village on Jakku. And they even go as far as to introduce us to Lor San Tekka so we actually like him a little by the time he's brutally murdered.
But the Imperial Stormtroopers accomplish a similar feat in Episode IV by wiping out an entire Jawa community in search of the escaped droids. As viewers, though, we're not allowed to watch the carnage and therefore aren't necessarily given the opportunity to respect their ruthlessness in the same way.