Something one should note is that Texas cities aren't quite like those in the Northeast- they sprawl out in a ridiculously huge way. I'm way out in the Houston suburbs, but I travel less than one mile away and I'm technically in Houston, even though the whole area is comprised of wealthy white conservatives. I bet if the suburbs that comprise a surprisingly large portion of Houston and San Antonio were removed the margins would be similar to other big cities.
Speaking as a Californian whose knowledge of Texas Demographics is limited to what i can find on the Internet, I think it's more that Houston just doesn't have many Liberal Whites. There are only a handful of White-majority districts that went for Obama in 2008, and they are almost all in Neartown and central Houston, basically. There's no Chicago's North Side, no Manhattan Island, no West LA, etc which is why a city that is only about 30% White votes 38% Republican. Though having heavily Republican Suburbs (North Houston is like 80% Republican from what I can tell) does certainly help.
San Antonio on the other hand, only leans Democratic because there's really not many black voters there. When Republicans win the White vote by only a little less than they lose the Hispanic vote in a city that's about 60-40 Hispanic, elections tend to be very close. And just by removing about 500,000 people's worth of the blackest parts of Houston (best estimates here, basically South, NW and parts of the NE), leaves the City 50-50.
Doesn't help that the older (majority) white working class areas, where Democrats do decent (though don't dominate a la Manhattan, obviously), are mostly
outside the city limits.