I have to agree with TunnelRat. I was of the opinion that you should use an inexpensive defensive ammo to practice with what you fight with.
But, if your defensive ammo has a similar Point of impact as your practice ammo, and similar recoil, I don't see the benefit.
There are some exceptions to this. Some of the super light weight bullets like the 85 grain 9mm defensive rounds that use non-lead materials or have special bullet designs outside the normal hollow points, I would argue, if you're going to use those for defense, you should get quite a few to train with.
But, the majority of normal bullet weight defensive loads (90-100 gr for .380, 115, 124, 147 for 9mm etc.), in regular SAAMI loadings, or even SAAMI +P loadings do not typically see a significant POI shift within 10 yards nor a significant recoil difference. Again, this can vary significantly if using non-standard bullet weights or non-standard pressures (+P+)
With .380 in particular, I don't believe many of the pocket guns are +P rated, so you are going to be constrained by SAAMI normal pressure which will limit recoil differences as well.
With that said, what is "new" about the Federal Punch compared to other .380 hollow point ammunition?