The water is brown b/c of the silt content of the rivers exiting to the Gulf of Mexico. There are however, stretches along South Texas that dont' experience that river dumping effect and are quite beautiful.
We've got plenty of bad beaches in FL too, people just don't visit them, or even know about them. It all depends on, like you said, silt, vegetation, currents, and depth.
Sometimes you get bad beaches, like Shell & Alligator Point in the panhandle, and then a few miles down the road on St. George Island, a really nice beach. Also, folks who haven't been there, think the Keys are loaded with great beaches, when actually there are only a few that have large expanses of nice sand. The beaches of Sanibel Island have been my favorite since the late 1970s, but even there only one side of the Island has nice beaches, the other side has mangroves right up to the shoreline.
I understand that Texas A&M has a study on how to change the currents in the Gulf of Mexico so that Mississippi River mud lands in Florida, not along the Texas coast. Their conclusion so far is that something in Florida must be repelling the mud, and the best candidate for that is all the plastic flamingo lawn ornaments in Florida.
Consequently, our Governor Rick Perry has decided his next project after the Trans Texas Corridor toll road is to buy 10 million flamingo lawn ornaments for Texas homes.