Fitness trackers, how accurate are they?

I've been looking at modern fitness trackers such as Fitbit and cheaper devices too, but I don't really get how they work. I currently use a device that relies on a band that I wear around my chest that measures my heartbeat and estimates calorie burn using data I have entered about my age, height, weight and gender. I have always assumed that this is more accurate than what I get from my runtsatic phone app, which knows my stats but doesn't measure my heart rate. Is this the correct assumption? There is always a big discrepancy between the two - runtsatic always thinks I've burned at least 50 calories more than my watch device (Bauer).
Modern devices appear to be just the watch part, with no heart rate monitor. Do they measure your heart rate from your wrist, or do they estimate calorie burn from your given stats? Also, do they alert you if your heart rate is outside the parameters you set for various types of exercise like my current device does?
Im not interested in a smart watch, I'd just like a good device that syncs with my phone without me having to enter data manually or wear the chest band, which can become displaced and is uncomfortable in very hot weather. Can anybody advise me here? I'm starting to think that the device I already have is probably better anyway and only cost about €30!