There are three factors: tint, flicker, and color rendering.
You're familiar with color temperature - that's essentially the orange-blue axis for white light, but there's also a red/green tint axis to consider. Humans vision is most sensitive to green light, and the lumen as a unit is calibrated to human visual sensitivity. You'll never guess what companies trying to add a few more lm/W to their efficiency rating do to the tint. Incidentally, one study I read that doesn't seem to be online anymore found people prefer tints redder than incandescent bulbs.
Flicker can come from running LEDs from AC, resulting in a low-frequency flicker that's very visible to more sensitive people. Incandescent bulbs change brightness much slower, so they're fine on AC. Another possibility is a power supply in the LED bulb that intentionally flickers the LEDs, usually at a higher frequency than mains power in order to control brightness with pulse-width modulation. Flicker-free variable constant current power supplies are available, but tend to be more expensive than PWM.
Finally, color rendering is affected by the spectrum of the light. An incandescent bulb has a spectrum that peaks at a specific wavelength and falls off relatively smoothly to the sides. LEDs can have a wide variety of spectra, often with many peaks and valleys, such that the two light sources viewed directly can look the same, but render colors very differently. A crude measurement of this is color rendering index, and many LEDs advertise theirs. 100 is the highest possible rating, and over 95 is considered very good.
The problem with CRI is it's based on a mere eight color samples, and leaves out some colors LEDs tend to be bad at. It's getting more common to see an R9 (deep red rendering) rating advertised. LEDs often do badly on R9, and there can be a big penalty to efficiency to achieve a high rating. Less commonly advertised, but also a common weakness for LEDs is R12 (deep blue rendering).
I care about this stuff and use an LED videography panel with adjustable color temperature to light my work environment. It's neutral to slightly reddish, flicker-free, has excellent CRI (97) and R9 (98). R12 is a bit weak (82).