My guess is that a metered taxi is much safer, as measured by death/injury per Km, than a UBER here. This is pure opinion, but is based on ~ 10 years of driving here (personal car) and seeing that anyone can buy a license (assuming they even have one). Taxi drivers have a vested interest in protecting their lives/taxi, while just about any Somchai can get behind the wheel of a car here.
When you factor in a knowledge of the roads - always amazes me how savvy you have to be to get around the Bangkok area ( a huge area) - traffic, routes, a taxi is probably safer and more reliable. Yes, they come with a few drawbacks, the main one seems to be dodgy fares, which is easily overcome by using GrabTaxi and paying 25 baht extra. Factor in the "legality" issue of UBER here and a taxi might win out 95% of the time?
An experienced, known good/reliable UBER driver, running a decent vehicle with a legitimate green plates and a valid driver's license would probably trump any taxi?