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Souvenir coins come from the regular production line at just one mint.
The full uncirculated mint sets have coins from both mints. They are made on different presses that run at a lower speed and higher pressure. They also get better handling.
All the souvenir set coins I've seen are just regular production runs. They seemed to make a little effort to get nicer coins and they tend to be a little less damaged but they are not made to mint set standards. This means there are some very beautiful coins in them but they aren't often fully struck by new dies. I've heard that some of the low mintage '90's sets have a few coins struck on burnished planchets and Gems but have never seen one. It was not a reliable source and mere hearsay but it was apparently said by someone who had one.
Speaking of beautiful coins there are some coins like the '80-D half dollar that comes highly Gem in the mint set but almost always has a shallow scrape on the reverse caused by mint set handling equipment. The souvenir set version never has this scrape but unfortunately almost every half dollar in this set has the normal dings and abrasions and is not often well struck. I have seen well struck mark free souvenir set coins however.
There are likely other such anomalies but my sample sizes are too small on most to make any determinations. I have however seen a lot of the '82-P and souvenir sets. Some of these coins are really nice Gems and I've even seen PL Gem cents in them. What I've never seen in one is a well struck Gem quarter. Strikes are atrocious on these and you can find a few without marking you can't find a crisp strike from a new die.
The '87 souvenir sets have some really nice half dollars that look a little different from the mint set coins. Some '77-P quarters are a sort of "matte" finish.
Souvenir sets aren't a great place to find Gems but they are a great place to find rarity, something different, and some really nice coins. These have never been very popular but there are a few very very avid collectors out there.
Time don't fly, it bounds and leaps.