For ITC you need much more material/higher concentrations than for SPR. For affinity constants, ITC is considered to be the gold standard, since you work in solution. In any case, your experiment needs to be carefully designed.

Depending on which metal you want to use, SPR might not be the best choice as some metals interfere with the detection, we observed this e.g. for lanthanides. Then, in the typical SPR machines you use carboxymethylated dextran surfaces that are charged which might lead to artifacts especially if your protein likes to bind to charged molecules, although I think this won't be a problem with DNA. In case your DNA is biotinylated you can easily try SPR by using a Streptavidin chip to immobilize your DNA. This experiment is straight forward and can be performed with low sample consumption. In any case, you should use at least an orthogonal method to validate your results.

In case the affinity of the protein to bind the DNA is low both experiments might become challenging because you will need a lot of protein or DNA. This is especially true if you don't have access to a microcal ITC or comparable. You have to make sure that your protein sample is in an appropriate condition to perform and survive these measurements at high concentration and that it will survive the measurements as well.

See above for very good comparisons between SPR and ITC.  I also agree that MST can be a good alternative, especially if you want low sample consumption and quick turnover.  Also consider biolayer interferometry as an alternative to SPR.