3g and LTE are on different bands so the signal strength will not be the same. 1 bar of LTE will be faster then full bars of 3g. And yes i agree PM is very quick,
Also, when making a call it will switch to 3g on your indicator because the call is using the LTE and then 3G for the rest of the stuff while on the phone
LTE, for the most part, is operating on Band IV 1700MHz. The signal on that doesn't travel as far as something such as UMTS Band V 850MHz that Public has available to its customers.
The signal reading measurements are reported differently for LTE compared to HSPA. I've noticed that LTE almost always shows 2 bars or so but it's still fast, and is even fine in indoor basements where I have tried.
Your phone will automatically use HSPA for voice service, or when there is lack of and LTE data signal.
I would just set your phone on automatic network type and not even think about it
When you have less bars your phone uses more power to use the signal. So in theory yes it will use more battery. But very margonally. I wouldnt worry about it.