Generally when a vendor gives a spec for gradient strength, they are referring to the maximum gradient an individual gradient coil can produce. However, as Samuel mentioned there are 3 gradient coils(X, Y, Z), if you pulse them simultaneously you get a gradient along the diagonal that is stronger than what any of the individual coils can produce. if you pulse the three gradient coils at 45 mT/m, the gradient along the diagonal would be 78 mT/m. So the vendor advertising this vector amplitude, is trying to make it sound like their gradient coils are stronger than they actually are.

Maximum gradient strength really only matters for DTI. The higher your maximum gradient strength, the larger the maximum b-value you can achieve at a give TE. Or conversely you can achieve the same maximum b-value at a shorter TE, if you have stronger gradients. The shorter TE means higher SNR. For DTI experiments, you want to use the same b-value in many different directions, so the maximum gradient strength of the individual gradient coils is the important number. For the system you have mentioned, 78 mT/m can only be achieved for 4 directions.

For other demanding pulse sequences, such as EPI, the gradient coil slew-rate is much more important than the maximum gradient strength. The optimum gradient amplitude for typical read-out gradient pulses or slice selection gradient pulses, is usually well below the maximum gradient that available gradient coils can achieve. However the slew-rates are all software limited in order to avoid peripheral nerve stimulation, so the vendors don't talk much about slew-rate.

Agree with comments here. Also: 1. In practice most sequences don’t actually hit 78mT/m; primarily diffusion gradients, and perhaps phase contrast and sometimes crusher gradients for FSE/TSE. 2. It’s sometimes helpful to compare pulse sequence parameters for the same protocol. For eg, the minimum TE from DTI/DWI would be important. The echo spacing from EPI and FSE/TSE could also be compared. 3. The duty cycle could also be important, as higher grad amplitude translates to higher current, which affects thermal considerations and could mean lower slices/TR in fMRI and DTI.

Agree with comments here. Also: 1. In practice most sequences don’t actually hit 78mT/m; primarily diffusion gradients, and perhaps phase contrast and sometimes crusher gradients for FSE/TSE. 2. It’s sometimes helpful to compare pulse sequence parameters for the same protocol. For eg, the minimum TE from DTI/DWI would be important. The echo spacing from EPI and FSE/TSE could also be compared. 3. The duty cycle could also be important, as higher grad amplitude translates to higher current, which affects thermal considerations and could mean lower slices/TR in fMRI and DTI.

Agree with comments here. Also: 1. In practice most sequences don’t actually hit 78mT/m; primarily diffusion gradients, and perhaps phase contrast and sometimes crusher gradients for FSE/TSE. 2. It’s sometimes helpful to compare pulse sequence parameters for the same protocol. For eg, the minimum TE from DTI/DWI would be important. The echo spacing from EPI and FSE/TSE could also be compared. 3. The duty cycle could also be important, as higher grad amplitude translates to higher current, which affects thermal considerations and could mean lower slices/TR in fMRI and DTI.