My first question would be, why worry about which is better/worse? Why not just get the best of both by combining them into a single tracker using my Composite Tracker? 
Looking at what you’ve done so far, and what you seem to be asking for, I have a couple more questions. Why do the two automations use different “for” values in the trigger? Isn’t that unfair? You also say, “I’d like the life360 timestamp to date from once I’ve actually opened my front door.” And how can that be determined? Do you have a sensor on the door?
I don’t know about the BT tracker, but the life360 one has a last_seen attribute which indicates the last time the location was updated. You could use that at least when the BT changes to home to see how stale the information from life360 is.
FWIW, I use life360 and google_maps on my phone and my wife’s phone (combined using the composite tracker.) I was interested in seeing which service seems to be quicker at noticing when we arrive or leave home. I wrote this:
notify:
- platform: file
name: composite_wife
filename: composite_wife.log
timestamp: True
- platform: file
name: composite_me
filename: composite_me.log
timestamp: True
automation:
- alias: Composite Updates Wife
trigger:
- platform: state
entity_id: device_tracker.wife
to: 'home'
- platform: state
entity_id: device_tracker.wife
from: 'home'
action:
service: notify.composite_wife
data_template:
message: "{{ trigger.to_state.state }}: {{ trigger.to_state.attributes.last_entity_id }}"
- alias: Composite Updates Me
trigger:
- platform: state
entity_id: device_tracker.me
to: 'home'
- platform: state
entity_id: device_tracker.me
from: 'home'
action:
service: notify.composite_me
data_template:
message: "{{ trigger.to_state.state }}: {{ trigger.to_state.attributes.last_entity_id }}"
This creates two timestamped log files showing which service switched the composite tracker to and from home. They each look like this:
Home Assistant notifications (Log started: 2018-10-21T13:53:22.917542+00:00)
--------------------------------------------------------------------------------
2018-10-21T13:53:22.917678+00:00 not_home: device_tracker.life360_wife
2018-10-21T15:39:28.723848+00:00 home: device_tracker.life360_wife
2018-10-21T16:05:56.547730+00:00 not_home: device_tracker.google_maps_nnn
2018-10-21T23:31:14.096787+00:00 home: device_tracker.google_maps_nnn
Then I wrote a Python script (I use outside of HA) to analyze the logs:
import sys
count_home = {}
total_home = 0
count_not_home = {}
total_not_home = 0
with open(sys.argv[1], 'r') as f:
for line in f.readlines():
if 'google' in line:
source = 'google'
elif 'life360' in line:
source = 'life360'
elif 'ping' in line:
source = 'ping'
else:
continue
if 'not_home' in line:
count_not_home[source] = count_not_home.get(source, 0) + 1
total_not_home = total_not_home + 1
else:
count_home[source] = count_home.get(source, 0) + 1
total_home = total_home + 1
print('home: total: {}'.format(total_home), end='')
for source in sorted(count_home, key=lambda x: count_home[x], reverse=True):
print(', {}: {}%'.format(source, round(count_home[source]/total_home*100)), end='')
print('')
print('not_home: total: {}'.format(total_not_home), end='')
for source in sorted(count_not_home, key=lambda x: count_not_home[x], reverse=True):
print(', {}: {}%'.format(source, round(count_not_home[source]/total_not_home*100)), end='')
print('')
Then using it on both of the logs I get:
pi@raspberrypi:/home/homeassistant/.homeassistant $ python3 composite.py composite_wife.log
home: total: 182, life360: 86%, google: 14%
not_home: total: 178, google: 50%, life360: 50%
pi@raspberrypi:/home/homeassistant/.homeassistant $ python3 composite.py composite_me.log
home: total: 179, life360: 77%, google: 17%, ping: 6%
not_home: total: 178, life360: 86%, google: 14%
The log files include data obtained continually since last October. As you can see, Life360 is generally better at more quickly updating when leaving or arriving home. Note that both services are running on both of our phones, at the same time.
One last comment about this data: You can see a small percentage of ping being the first indicating I was home. This is from when I ran that service for both of our phones as well as the others. It made such little difference I ended up scrapping the use of the ping device_tracker.