Hi,
Check dropout voltage graphs and PD in datasheets.
TPS73801 (I'm familiar with it) shows 100mV at 25ºC and 150mV at 125ºC for 200mA out, but that is with Vin = Vout, I guess that may work for you, the PD formula at the bottom of the datasheet is worth going through before buying the wrong part; also the TPS793 from looking at dropout voltage in the datasheet, ditto PD calculations. TLV701/2/3/4, perhaps not, as 701 and 704 are only 150mA.
Best suggestions for LDOs are suffering an hour or so comparing on manufacturer product pages using the filters to narrow the options, and reading a few datasheets. LT may have something with a cherry on the top you really prefer over something TI offer, or maybe ST or Intersil have something better/cheaper, or the same but more expensive, and so on. Really good to browse a few datasheets and make a personal informed choice, then check back if you have any doubts.
I like Micrel LDOs, but I wouldn't use them in everything, it would be a waste of money sometimes, I like the TI TPS73801 as it is idiot-proof/indestructible, but you may not.
All this said to help, as reading datasheets and comparing price/ku is very informative. TPS793 presumably fine.