GPS v.s. RTK (HERE+RTK)

Just to clarify, when you say

What exactly are you referring to?
Is it L1 only (single frequency) GNSS units?
The Here+ is a single frequency GNSS unit.

If it is then what you are seeing is about as good as it gets for single frequency GNSS units.
It only when you go to multi frequency that you will start to see improvements in positional accuracy and lock time.

You have probably seen these topics but I am just throwing them in here, there maybe one or two you mightn’t have seen.

RTK and general GNSS inaccuracies

A bit more in-depth here

Finally Spilling the Beans on RTK GNSS

An evaluation of Here+

Arducopter RTK GPS: Quick position and altitude precision evaluation

RTK - Useful or not?

A good comparison

Quick Here+ vs Reach vs Septentrio RTK

RTK GPS Precision Navigation

And a good write up by Tridge

Comparing a uBlox F9P with a M8P with RTK