Equivalent series resistance vs. parallel leakage conductance
This relationship does apply not to all caps.

The leakage is usually defined as a current max or Rp at Vmax at some fixed temperature. (Not \$G_e\$).
We know that Plastic caps are closest to ideal with very high
\$\tau_{leakage}=R_p*C\$ and very low \$\tau_{conduction}=ESR*C\$
for all caps there is a SRF with Zmin(f) series inductance XL(f) that matches the impedance of  C,  Xc(f) for a series resonant frequency (SRF) after which Zc(f) rises with frequency.


Note : SRF is often called Self-Resonant Frequency for parallel tank ccts. But for RF some cap suppliers prefer to call this PRF for parallel. Don’t let this confuse you, it is a label than has been “grand-fathered”.

So the two time constants may have some ratio within only the same P/N family of dielectric parts. Plastic or Metal Film vs Ceramic vs NPO ceramic vs Aluminum Electrolytic (e-caps) vs Double Electric Layer Ultracaps and batteries all have different ratios and values of the two different time constants.
You may make a spreadsheet of different dielectrics to see how this varies.
I have done this for e-caps and found that in most cases, standard (cheap) e-caps have an ESR * C time constant of &gt;&gt;100 us, while “Low ESR” e-caps have this time constant 1 to 10 us. ESR does reduce with rising voltage ratings somewhat but not as significant as the dielectric/terminal interface related ESR which affects cost. Also, I have noticed, they specify Dissipation Factor, DF and no ESR, then it has always been a “standard cap” when used with storing rectified line frequency pulses thus specified at 120 Hz (industry std.) so Beware for SMPS caps.

for same value of say 1uF ceramic caps tend to be slightly lower ESR than low ESR caps but in the &lt;100 pF range NP0/C0G caps are much better with lower density and smaller max value.
Plastic caps with a much lower dielectric constant have a very low leakage and lower ESR so the two time constants are far apart making them more ideal, yet far more expensive in large values as well as size.
loss tangent is certainly used for RF especially above 300 MHz and becomes critical for FR4 at &gt;=1GHz to choose a low loss tangent material and NP0 caps.