How do servers with redundant power supplies balance consumption?

I have several servers from the HP DL360 line (generations 5-8). Each of these servers has two power supplies installed. The 2 power supplies in each server are fed from different circuits.

My question is will the power draw be roughly balanced between these two circuits, or do the servers consider one power supply to be a "primary" and the other to be a "backup" with a smaller power draw?

I'm going to give an HP Proliant-specific answer here, since the OP is asking about the HP product line.

Let's use the example of an HP DL360p Gen8 (also applies to G6, G7 and Gen9 servers):

You have the option to configure the Redundant Power Supply Mode in the HP Rom-Based Setup Utility (press F9 at boot) with:

• Balanced Mode
• High Efficiency Mode

Of the two main options, there's some granularity in the High-Efficiency Mode:

• High Efficiency Mode provides the most power efficient operation with redundant power supplies by keeping one power supply in standby mode at lower power usage levels.
• Balanced Mode shares the power equally between both power supplies.
• In addition, the "Auto" mode chooses between one PSU or the other as primary, depending on the serial number. It's a way to randomize the distribution in a datacenter situation with multiple servers.
• Also see: Maxing out both PDUs in a rack with redundant power

An example of the Balanced Mode on a busy server:

hpasmcli> SHOW POWERSUPPLY
Power supply #1
    Present  : Yes
    Redundant: Yes
    Condition: Ok
    Hotplug  : Supported
    Power    : 110 Watts
Power supply #2
    Present  : Yes
    Redundant: Yes
    Condition: Ok
    Hotplug  : Supported
    Power    : 95 Watts

An example of the High Efficiency Mode on an idle server:

hpasmcli> SHOW POWERSUPPLY
Power supply #1
    Present  : Yes
    Redundant: Yes
    Condition: Ok
    Hotplug  : Supported
    Power    : 50 Watts
Power supply #2
    Present  : Yes
    Redundant: Yes
    Condition: Ok
    Hotplug  : Supported
    Power    : 20 Watts

An example of the High Efficiency Mode on a busy server:

hpasmcli> SHOW POWERSUPPLY
Power supply #1
    Present  : Yes
    Redundant: Yes
    Condition: Ok
    Hotplug  : Supported
    Power    : 90 Watts
Power supply #2
    Present  : Yes
    Redundant: Yes
    Condition: Ok
    Hotplug  : Supported
    Power    : 20 Watts

Detailing the relative efficiency of single PSU, load-balanced PSUs and High Efficiency mode on a 750W power supply.

it depends

If you go into setup (F10) you can choose the power management mode and usually there's a few options including the active/passive options you suggest as well as a balanced mode. I buy blades and you do this at the blade-enclosure level and there seems to be more options but essentials it depends :)

Every server is different. Some automatically balance between the two and some use the primary PSU exclusively until it fails and then switches to the secondary PSU. In most cases there is a bios option to configure how the server treats the PSU's. If for some reason you don't have that option you can find out by putting a clamp ammeter on each power cable and measuring the current draw.