Thanks for the explanation. So if I understand correctly. The RG213 is better shielded than the RG8/X that's why I'm seeing higher SWR's?
It is more than just the shielding, the material used between the center conductor (the dielectric), length, as well as other factors also affect this. But when all the parts come together the lower loss in the feed line will show a higher SWR, and its readings are closer to where the antennas SWR actually is as well. The exception is if there is an issue with that coax itself, (cold solder joint, kink, ect.) which is entirely possible.
Think of it this way, your radio transmits a signal, which then goes into the forward side of your SWR meter at full strength. Then as the signal travels down the feed line towards the antenna the feed line losses will attenuate the signal (or make the signal weaker). How much depends on the loss characteristics of the feed line and how long it is. When it gets to the antenna that does not have a perfect 1:1 SWR match, a portion of the signal is reflected, and travels back up the feed line. As it travels back up the feed line it is attenuated again just as before. This signal is the reflect reading on your SWR meter.
The SWR reading, being a ratio of forward power to reflected power, is affected by this loss. As the loss only affects the reflect signal, it will have a lower reading, while the forward reading will be unaffected. You can get around this by putting the SWR meter at the antenna feed point as I mentioned above.
All that being said, either of those coax lines that you used should have an insignificant amount of loss at the length that you are using. I can do some calculations and get some percentages for you if you wish.
The DB