BK Precision 1550
This is a switching supply.
The up-down adjustments would make this a non-starter for me.
CSI3005X5
A whole bunch of companies re-brand this unit. They're actually fairly decent. The voltage pot is a 10 turn, the current limit is button-driven in 0.03A increments.
The most common resaler of the power-supply is MPJA. It also comes in a bunch of voltage and current ranges: 0-30V 5A, 0-60V 3A, 0-120V 1A.
One thing you can't see in the pictures is that the unit has a set of screw terminals in parallel with the output banana jacks, below the cover plate labeled "EXT OUTPUT". If you need more permanent connections, you can use the screw terminals.
The schematic for the whole supply is available. This makes it enormously more repairable (and hackable) then ANY of the others.
BK Precision 1671A
The funky extra output connections on this make me nervous (speaker terminals? really?).
I would guess that the potentiometers are single-turn, both from the artwork on the case near the knobs, and the fact that it does not mention multi-turn knobs, as that's normally a significant selling point at this price range.
On the whole, If I had to choose from the supplies listed, I would wholeheartedly recommend the CSI3005X5, more because the alternatives are considerably worse.
Anyways, I would say that even if you don't think you need a floating output power supply (what you really mean when you discuss a separate earth terminal), you almost certainly will find it useful in the future, so I think you shouldn't dismiss it. Just being able to string multiple power supplies in series for higher output voltages is tremendously useful.
Because the supply is floating, and you only made one measurement at once.
Floating means isolated, which means the resistance between the supply and ground is very very high. So high that the 10 Mohm input resistance of your multimeter is almost a short circuit in comparison.
simulate this circuit – Schematic created using CircuitLab
If you were to make both measurements at once, with identical meters, you would find V- at -6V and V+ at +6V with respect to ground, and 12V of course between V- and V+.
Best Answer
Your switching supply output is isolated from the input via it's transformer. It also has a plastic case which should have a double insulted symbol on it somewhere (two squares, one within the other) This means the output is "floating" (i.e. not referenced to earth)
Never tie the mains neutral to earth, they both serve very different purposes. Although they are actually tied together at the house's input (in most house wiring systems), the neutral is for return currents and the protective earth is for detecting fault currents and keeping (metal) equipment cases at a safe potential.
You sometimes see plastic cased switching supplies with an earth lead, which is usually used for the EMI filter and to reference the output to earth. Sometimes tiny leakage currents through the transformer windings (or the EMI Y caps if the earth is left unconnected) can charge up the output (relative to earth) to a reasonably high voltage, enough to give you an annoying (but safe) zap when you touch one of the terminals. The earth can be used to drain the leakage currents.
So you can tie the isolated output to earth if you wish, but just use the L and N connections as directed on the mains side.
Further reading:
Safety Considerations in Power Supply Design
Power Supply Technical Guide - also deals with other aspects unrelated to the question, but very thorough and detailed.
UL1310 - Class 2 Power Units
UL1012 - Power Units Other Than Class 2