bars mean ****. the carriers and phone manufacturers can manipulate the bars. Lets say you have 5 bars. 1 is bad, 5 is awesome. your cell reception is measured in dBm like you(forgot to quote person) stated. your iphone and note3 can be getting -85 dBm but the iphone might display 4 bars while the note 3 displays 2 bars. Your signal is -85, they are the same signal, the companies manilpulate the data to make their service/product better.
Case in point Google put out the galaxy nexus 2 yrs ago and with that same "good" signal, the phone displayed 2 bars max, rarely 3. From what I read, the nexus was displaying the true bars for that signal while other phones typically display inflated bars. Believe it or not, either google or verizon caved and in an update, started showing inflated bars for the same signal. This was due to a placebo effect where everyone thought their signal sucked because they had 1 or 2 bars. I never dropped a call on that phone despite having 1 bar most of the time
so what you need to do is compare those dBm numbers between the phones. Lower is better I believe.