Basically two types of tilt sensors in these devices.
Old style single axis ones like the Wixey have a pendulum and angle sensor. Tilt it, the pendulum swings and the sensor says how far. Simple, easy to understand and fundamentally accurate but they do need to be well made. You do need to be aware of axis orthogonality issues when making measurements of small angles. If its not directly aligned with the tilt axis funny results are possible. Fundamentally a good technology but, as ever, the consumer variants are "made too cheap". No excuse for the flat battery issue. Electronic variant of the Dumpy and Cowley levels really.
Two axis ones and some more modern single axis ones use MEMS (Micro-Electronic Mechanical System) devices. Silicon chip technology applied to itsy bitsy teensy mechanics. Basically they measure the acceleration due to gravity which changes when you tilt the device. According to MEMSIC "the amount of acceleration due to gravity in 1 arc-degree of inclination from a horizontal plane is 0.017g. In order measure to within ±0.3 arc-degree the accelerometer must be accurate to within ±0.005g".
Not a lot.
The results you get are very dependant on the software in the device. Lots of calculations going on to make it behave due to the inherent non linearities and cross coupling over orthogonal axes. No reason why an inexpensive device can't be good but phone devices can be notoriously badly behaved due to poor software. Pure laziness really as the maths is well understood and any decent MEMS sensor will be well characterised but if the phone OS folk can't be bothered to get it right, with much more resources than an inclinometer maker, whats the chances of getting a bad implementation in your Amazon/E-Bay/Ali-Baba bargain.
Its not difficult to check the performance with very simple equipment. Just monumentally tedious. Wave goodby to a weekend basically. For fairly obvious reasons worst errors will probably be at small angles but you have to check the whole darn thing as there is a lot of maths going on. Hidden gotcha is how well the sensor is aligned to the axes of the body.
Clive