Either is a good choice for visiting SA.
If you do decide on Braunig, try for their premium sites. Much better than the regular and $25 a night PA Rates.
Also, if you use Braunig, or anywhere else and you want to drive into SA. Almost directly behind The Alamo is an all day parking lot for $10. I used to use it with my F350 long bed, Crew cab, King ranch with no problem at all. The Street in front of the Alamo is one way, so the street just before The Alamo, turn right (E Crockett St), then follow around the curve and take the very next left(Bonham St). That will put you directly behind The Alamo. Proceed down that street and you will see the parking lot on the right, but you have to turn right (E Houston St.) on the next street for the entrance.
Parking Lot Click on Birds Eye View and zoom into the parking lot, or just drag and look around.
One of The River Walk entrances is across the street from The Alamo.
We will be in the SA area from May 4 through May 16 at Fr. Sam Houston, then down to Corpus for a Week at the NAS.
Happy Trails.