They are similar in theory, but different in application.
First, lets take a close look at the wording of each.
If you are successful, an observer can't tell that you're casting a spell. That observer cannot make an attack of opportunity against you for casting, nor can it attempt to counter your spell.
Sleight of Hand
When casting a spell, you may make a Sleight of Hand check to make your verbal and somatic components less obtrusive, muttering magic words under your breath and making magic gestures within your sleeves.
Now, the first big difference between the two are:
Skill Trick vs. Skill
Skill Tricks can only be used once per encounter. Skills can be used multiple times during an encounter.
Now, the second big difference between the two are:
Casting Unnoticed vs. Casting Less Obtrusive
The Skill Trick allows you to cast the spell, and if successful, without allowing others to realize you had casted a spell.
The skill allows you to make the Verbal and Somatic components go unnoticed, however, Material components and Focuses are not mentioned.
Therefore, if a holy symbol is a focus for a particular spell, an opponent may not notice you are casting a spell, if successful, however, they may know you are "doing something" since you are using your holy symbol in a way that is not typical.
Same with a material component. An opponent may not notice you casting a spell, but if a gem or other material component is seen being taken out of a bag, and suddenly disappears, they may not realize you had just casted a spell, but they may know something is amiss.
The Skill Trick, if successful, will not allow counterspelling, since your opponent doesn't even realize you casted a spell.
The skill, if successful, doesn't guarantee an opponent won't counterspell you, since he can still notice an arcane or divine focus, and a material component. A proper Spellcraft check could give an indication of what spell you are about to cast, depending on the focus and material component present.
Once per Encounter vs. Once per Opponent
The Skill Trick will have more application when going up against someone that you know for a fact is readying an action against you for spellcasting - such as a counterspeller or a 'mage-slayer'. But since you can only use it once, make sure it is with a spell that is worth it.
Also, the Skill Trick could have good roleplaying potential. For example, if you want to Suggest, Charm, or Dominate someone without anyone, especially the target, noticing that you are doing as such.
The skill, will have more lasting application, especially if you are using spells that do not have a focus or a material component. Using the same examples above, Suggestion does have a material component, but Charm Person and Dominate Person do not.
The skill, will also have more lasting application, since it isn't limited to once per encounter. It also allows you to try again, albeit with a penalty. The Skill Trick, whether a success or a failure, is used up for that encounter.
If you are going to do one, may as well get the other. The Skill Trick would cost you two skill points. Unless you are a spellcaster that has Sleight of Hand (Bard,
Spellthief, etc), one rank of Sleight of Hand will cost you two skill points.
Bards, typically being a face, may find better usage out of the two, particularly with charming and suggesting. The bard may not want the merchant to realize he was forced to be a friend and give the party a better deal than he normally would, or for that matter, another customer or a security guard standing next to him.
Also, for their own health, wizards and sorcerers may not want the Big Bad Evil Guy to know that it was them that just cursed him and/or his forces. A cleric and a druid may also not want the Big Bad Evil Guy to know that is was them that had healed the party to full.