How does the Bedtime Bulb compare to Philips' "warm glow" bulbs, which also adjust their color temperature as they dim?

The Philips bulbs are more general purpose bulbs that would replace your "soft white" 2700K bulbs. I think they dim down to around 2200K. Otherwise, the specs are pretty typical for LED bulbs in terms of color quality, flicker, and dimmability.

Bedtime Bulb v2 starts at 2100K, much warmer, and dims down to 1700K. BBv2 has infrared. The flicker is very low: under 1% at 120 Hz; the best I have seen in any dimmable bulb. It is also designed to dim perfectly with all TRIAC and ELV dimmers (basically, any standard dimmer), which no other LED bulb can claim to do.

Side note: the term "flicker-free" is a total lie, so we stopped using it. I have seen lighting with up to 50% claiming to be flicker-free. Pretty much all lighting has some flicker. The term is just not true.