Which Color Card to Use?

If you already have one, then I recommend that use that one. The differences between the results of using MBR Color Corrector 3 with any of the cards are minor. But, if you don't have a color card yet, then there are some things to consider:

Practical Concerns

The biggest concern is the size of the card, for example the size of the card you need for close up talking head style shots will be smaller than that required for drone shots. Additionally, some of the cards come with cases to prevent damage to the card when not in use.

The various color cards have the following approximate sizes / cases:

Datacolor SpyderCHECKR    31 x 23 cm,    comes with a hard case
Datacolor SpyderCHECKR 24 23 x 14 cm
X-Rite ColorChecker Classic 4 x 3 cm (Nano)
9 x 6 cm (Mini)
28 x 22 cm
54 x 38 cm (XL),
XL size optionally comes with a soft case
X-Rite ColorChecker Passport Photo 11 x 7 cm, comes with a very durable hard case
X-Rite ColorChecker Passport Video 11 x 7 cm, comes with a very durable hard case
X-Rite ColorChecker Video 28 x 22 cm
54 x 38 cm (XL)
XL size optionally comes with a soft case
X-Rite ColorChecker Digital SG 28 x 22 cm

In practice the 28 x 22 cm X-Rite cards and the 32 x 23 cm Datacolor SpyderCHECKR card are about the right size for most normal footage.

Cost is another practical concern, the X-Rite XL sized cards, and the X-Rite ColorChecker Digital SG are much more expensive than any of the other cards.

Photo or Video Color Card?

When using MBR Color Corrector 3 it doesn't really affect the quality of the results if you use a photo or a video card.

Internally MBR Color Corrector tries to match the color patches on the card to known / reference values, and it treats every patch as equally important. This means that choice of a video color card will slightly bias the color correction towards getting skin tones correct, at the expense of other natural colors. (This is because, video cards have more skin tone examples and proportionally fewer other natural colors).

Photo Cards

In 1976 the Gretag Macbeth Charts were designed, and now that design of card is the X-Rite ColorChecker Classic. The chart’s color patches have spectral reflectances intended to mimic those of natural objects such as human skin, foliage, and flowers. A set of greyscale patches are included to help exposure settings, and a set of primary/secondary colors are included that represent colors not usually found in nature.

The Datacolor SpyderCHECKR 24, X-Rite ColorChecker Classic, and X-Rite ColorChecker Passport Photo are all photo cards. In all cases they are similar to the original Gretag Macbeth cards. (The newer X-Rite cards use slightly different ink and the Datacolor SpyderCHECKR 24 has very similar color patches in a slightly different order, but it is effectively the same).

Video Cards

In 2015 X-Rite released the video cards. The X-Rite ColorChecker Video and X-Rite ColorChecker Passport Video, when compared to photo cards have:

Some of these patches should make it easier to set you camera up while shooting:

Combined Photo and Video Cards

Two cards have the additional features of a video card without loosing any of the color patches found on the photo cards:

The Datacolor SpyderCHECKR contains (in the right hand pane) the original 24 photo color patches, and has 24 video color patches in the left hand pane. These extra patches contain a collection of skin tones, extra shades of gray, and the desaturated colors around the color wheel that are useful with video cards while shooting.

The X-Rite ColorChecker Digital SG contains (in the upper middle) the original 24 photo color patches, and around it about 100 more patches. These extra patches contain many skin tones, and many many fairly saturated colors from around the color wheel to show exactly how a camera responds.

My Personal View

Personally, I would recommend the Datacolor SpyderCHECKR (with 48 patches) for most uses, and the X-Rite ColorChecker Passport Photo or Passport Video if you shoot almost exclusively close up "talking head" shots.

The Datacolor SpyderCHECKR (with 48 patches) is effectively a photo chart and a video chart combined in a sensible size for most shots. The X-Rite ColorChecker Passport Photo / Passport Video are smaller and therefore ideal for close up shots.

All three of these cards come with a reasonable hard case, which means they have a reasonable chance of remaining undamaged in a kit bag.