I am experiencing the same issues with my iPhone 6 Plus 128gb on Verizon. Incredibly slow speeds on LTE (1mbps down .02 up), weaker wi-fi signals than my iPhone 4, and constant service fluctuations (no service, LTE/3G/1x coming and going sporadically).
I have been working to solve the issue with Verizon since I activated my account on 1/16/2015. No one on Verizon's end seems to know why the device is running slow. They claim I have impeccable LTE coverage in my area. I had to follow the typical protocol of resetting Network Settings, airplane mode toggle, restarting the phone, restoring the phone (both from back-up and as new iPhone without signing into Apple ID) nothing worked. When Verizon finally sent my claim to their diagnostics team, they tested various devices in my area and the results supposedly came back positive on their end. Now, finally, I am in the process of having my iPhone 6 replaced. I will update my post if I find that it was a device specific issue. Otherwise, I will be forced to cancel my account and return the product as I am within the 14 day return period. My girlfriend's Samsung Galaxy s5 has consistently good speeds on LTE and has been much more reliable. At this point I may just make the hop to Android.
I certainly hope it is a software issue and not a hardware issue. I've enjoyed apple products for a long time but this is absurd. It may also be worth noting that I managed to pull 44mbps down and 20mbps up on LTE at the verizon store. However, I haven't seen those speeds anywhere else. I don't believe this is a carrier issue as many others have reported similar problems across all carriers.