The Scottish Boinc Team

Whereas the original single-core ARM11 Raspberry Pi Compute Module was, in my eyes, a complete dud and I never saw the use -BOINC-wise- of owning one, this changed with the introduction of the Turing Pi at the end of the economical life of the original Raspberry Pi Compute Module's form factor, by then the Raspberry Pi Compute Module 3+.
You could cram up to seven compute modules on a board the size of an mini iTX board, giving you a 28-core ARM computer cluster(!), but with all the limitations of the original Compute Module, being not enough RAM per core, the needed six-rail PSU limiting the CPU speed, no PCIe, etc.

So then came the much more powerful Raspberry Pi Compute Module 4 (in short: CM4) and every Tom(my), Dick(y) and Harrie(t) went out of his/her head and designed their own carrier boards or embedded designs. Jeff Geerling keeps a nice database for it. There were also some who thought "better a good copy than a bad original design" and made modules with the same form factor as the CM4, but with additional connectors for extra features, so that their Compute Modules fare better on their own carrier boards than on those of others. As each module needs a carrier board anyway that actually isn't too bad, you just have to make sure you are not limiting your module by your carrier board

These are the Raspberry CM4 (compatible) modules at the moment (updated with the oddball -no GPU- RK3582 Radxa CM5 Lite):
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Condensed by connector format:
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Geekbench scores, mostly for those Compute Module boards that Jeff Geerling tested:
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The six-core Banana Pi BPI-CM4 and the eight-core Orange Pi CM5 and Radxa-CM5 modules take the top marks, but keep in mind that only the BPI-CM4 can truly be fitted on a Raspberry Pi CM IO board with full compatibility and that -while it can be run from the Raspberry Pi CM IO board- the Radxa-CM5 really prefers its own 3x 100 pins Radxa-CM5 IO board - even the older 3x 100 pins Radxa-CM3 IO board won't do, while the Orange Pi CM5 also does best on its own 3x 100 Orange Pi CM5 Base Board

Now that Raspberry Pi.org have their own successor to the Raspberry Pi CM4 (right) with the Raspberry Pi CM5 (left), I'd like to review some of the rest of the 'click-em-on compute module' field. Most of them (approx. 10 out of 20) follow the by now standard Raspberry Pi CM form factor: 55mm x 40mm (2.1'' x 1.5''), two 100-pin Hirose connectors and an ARM SOC (System On a Chip). There are some exceptions though.

The most obvious two exceptions are not only bigger, but feature no less than four 100-pin Hirose connectors: The the Rockchip RK3568 equipped Radxa CM3I (I for Industrial, having a huge IO board with lots of connectors) and the FriendlyElec CM3588.
Of these two the FriendlyElec CM3588 has by far the superior performance in CPU, GPU and NPU. The standard FriendlyElec IO board is meant for a NAS but, if the future ever is going towards a BOINC application that can make use of M.2 PCIe NPUs like e.g. the Hailo8 or the DeepX DX-M1, this FriendlyElec IO board can be a real AI monster, having space for up to 4x 26 TOPS of those AI modules.
But...for the time being, only its RK3588 really works in BOINC.

Another two differing from the mainstream are the Milk-V Mars CM and the Banana Pi BPI-CM6, that both have a RISC-V SOC. And while the somewhat lackluster Mars CM has a quad-core StarFive JH7110, the BPI-CM6 has an octo-core SpacemiT K1, promising somewhat more performance. It needs three 100-pin Hirose connectors to be fully operational, unlike the Mars CM that can do with the standard two. BOINC-wise, both have nothing to offer yet as none of he projects have native RISC-V apps. You might try Anonymous platform though to get tasks.

An odd one out is the Radxa CM5 Lite, that has a video-less SOC (hexacore A76(2)/A55(4) Rockchip RK3582), so do not expect a video signal here -but BOINC can't use ARM GPUs yet anyway. It also does need three 100-pin Hirose connectors to be fully operational though, perhaps because of the 5 TOPS internal NPU. I hope it uses the same IO Board that is in use by the Radxa CM5 (see below).
Boinc-wise this should outperform the Raspberry Pi CM5 by virtue of the two extra CPU cores, albeit mere Cortec-A55s.

Shortages of the Raspberry Pi CM4 led to 3D-printer manufacturer BigTreeTech (Biqu) making two CM4 interchangeable modules of their own. The first was the BT-CB1, which is the weakest performing ARM CM4-format compute module with its four Cortex-A53 cores. The following BT-CB2 is hardly better with four Cortex-A55 cores.
I still have to wait for positive reviews of two BT-CB2-like modules, having the same Rockchip RK3566 SOC and two 100-pin Hirose connectors : the LuckFox Core3566 (see here) and the Pine64 SOQuartz (a little bit better here).
There are two more RK3566 compute modules: the 2x 100 and 1x 24 pin Hirose connectors Orange Pi CM4 and the three 100-pin Hirose connectors Radxa CM3. The Radxa CM3 IO board seems to have all the troubles in the world, so Radxa came out with a RK3568J equipped Radxa CM3J that has two 100-pin Hirose connectors and can be fitted in e.g. the Raspberry Pi CM4 IO board without(?) problems.
BOINC-wise, the RK3566 modules have little to offer, if they can get to work at all.

The problems with the three 100-pin Hirose connectors hopefully will not re-emerge with the Radxa CM5. It has an octo-core RK3588S and was quite favourably reviewed by Jeff Geerling.
Like the FriendlyElec CM3588 an interesting option for its sheer computing power, ARM-wise.

There is yet another Hirose connector configuration in the wild: two 100-pin plus two 70-pin connectors, that is used with the Banana PI BPI-CM2 (with quad-core RK3568) and the far superior Banana PI BPI-CM5, another RK3588 compute module.

Have I mentioned all 'click-em-ons except for the Raspberry Pi models'? No, I have left out two modules, both with the standard two 100-pin HIrose connectors: the Banana Pi BPI-CM4 (Amlogic A311D A73(4)/A53(2) hexacore) -so comparable with e.g. an Odroid-N2/N2+, and the Banana Pi BPI-CM5 Pro a.k.a. ArmSoM-CM5, (with Rockchip RK3576 octo-core Cortex-A73/A53).
The latter should also be good to use in BOINC projects that make use of ARM boards.