You can do some work to narrow down performance, but you'll need carrier help if you find that there's an issue with one device.
- Use Safari to do a speed test http://fast.com on both devices - even if you are using different devices, different cell towers (just because two phones are in the same place - they can negotiate different frequencies, different towers or get different levels of service from the same tower at the same frequency).
By focusing on measuring the flow of data - you can over time know if one device has hardware limitations or hardware issues.
Next, put each device in field test mode: Dial *3001#12345#* - if you can see in the menu bar a number like -76 then record those for each device and then call your cellular company to help determine if you have coverage issues or need to update your phone's settings or software.
_Note: not all carriers have a useful field test mode. See this and this and that for more details.
Basically, each cell tower is a time share. It juggles all the devices in range - tells some to be on LTE, others to be on 3G, others to be on EDGE. Unless your phones don't work at all - the cause of differential service is almost always a device that's stuck and needing reboot or a congestion issue on the carrier end. Apple can also run diagnostics if you believe the hardware is faulty - but that's usually a low chance of being the cause.