I believe that the previous answer is a bit glib. There are a host of advocates of Pople basis sets and the answer to your question is more nuanced. The Karlsruhe def2 basis sets were optimized with DFT in mind; the Pople basis sets predate widespread use of DFT. Nevertheless, one can find Pople basis sets that are comparable to the def2 sets:

https://molssi-bse.github.io/basis_set_exchange/index.html

Both use some confusing naming conventions. The Karlsruhe basis sets may be slightly more efficient for DFT calculations but I doubt that there are huge differences in computational expense as they utilize the same gaussian orbitals. (I have used both sets and did not notice significant differences in execution speed.)

Metals are particularly difficult to compute and generally require polarization and diffuse functions, which are expensive to include. If you have limited computational resources, you might consider leaving out triple zeta orbitals and performing your calculations with double zeta orbitals but more polarization and diffuse functions. You'll have to do some calculations to get an idea as to the effectiveness and achievability, given your resource limitations.

Finally, what have other investigators used in your system? You may observe that the basis sets employed have evolved over time, reflecting the advances in computational power. To publish your results, you will want to be consistent with current usage; otherwise, you will find that reviewers are critical of your results.

Much appreciated for your detailed response Mark A Cunningham .

I am performing DFT calculation for one coordination polymer, and the choice of the basis set is an important point.

As I have seen, in a metal complex, that many researchers are using the def2 basis sets of the Karlsruhe group for the metal and other small basis sets for simple atoms, I needed to understand why exactly this type of calculation with several basis sets.

I don't have problems with computational resources, I can perform the calculation with any basis set as long as it's efficient for my system.

All the best

Historically, Pople and crew were most interested in biochemical systems: HCNO mostly. Metals are poorly represented in 3-21 or 6-31 bases. More recently, people have become more interested in metal enzymes and the like and a significant effort went into the development of bases like the def2 set, that can support heavier metals efficiently. So, it's not uncommon to see people mix and match, using 6-311+g* for HCNO and some def2 triple zeta basis for metal atoms that are not included in the Pople suite. You can always customize your basis choices, just be ready to defend any particularly odd choices.