Hide and Move Silently are now one skill, Stealth. A nice perk for rogues; a nicer perk for those who don’t have 8+Int skill points and still want to be sneaky. Also very nice that it’s only one roll: less chance of rolling very low and messing up your attempt to sneak. Or, if you do roll high, you don’t have to worry about having a mediocre roll on the other.
On the flip side, Spot and Listen have also been consolidated into one skill, Perception. This is still to your benefit when you’re sneaking, though, since it means those trying to find you only get to roll one check; there’s less chance of an abnormally high roll.
Changes to the effect of Hiding
In 3.5, the effect of hiding was left vague until Rules Compendium. Thankfully, Rules Compendium clarified some things, including the fact that those who fail their Spot check treat you the same way they treat invisible creatures, which means they are flat-footed with respect to you. This is important because that’s one of the conditions that qualifies for Sneak Attack.
In Pathfinder, not so much: a successful Stealth check gets you Concealment. In most cases, this is basically useless because you usually need Concealment to use Stealth in the first place. That is, Stealth is often literally giving you what you already had. You can use Stealth with Cover instead of Concealment, in which case you get both, but Cover is much more difficult to manufacture, which makes it much less reliable.
With Hide in Plain Sight, you can give yourself Concealment when you wouldn’t have had it. That’s nice, but the costs of getting Hide in Plain Sight are very high, and Concealment just isn’t that good. All Concealment does is give attackers a 20% chance to miss you. It does not improve your attack or damage in any way. Notably, Concealment is insufficient to trigger Sneak Attack.
Changes to triggering Sneak Attack
On the plus side, constructs, plants, and undead are no longer immune to Sneak Attack. Elementals and oozes still are, as are the new proteans, and things with the incorporeal subtype are immune unless you have Ghost Touch. The 3.5 rogue could overcome these limitations, but it was tricky (required particular wands or feats or ACFs, and often still only did half damage), so this is good.
The good news ends there. As stated, Stealth cannot trigger Sneak Attack. Nor can grease in most cases (and the rules are ambiguous about the cases where it would work), and the blink spell is right-out. Alchemical weapons no longer work either, which is a shame for low-level rogues. Marbles no longer exist. That means a lot of the ways for a solo rogue to generate the conditions required to get Sneak Attack are gone.
As such, you are either going to have to ignore the “Sneak” aspect of Sneak Attack entirely (and just use Flanking to trigger it), or you’re going to need magic, preferably greater invisibility. Rogues get Use Magic Device, but that’s an expensive wand.