I might not be the best person to ask because I'm a newb and have no experience with either bike but since no one else has responded yet, I'll give my opinion. h:

As others have said, if you've got enough self control (and I've even heard old men say they don't) to not go beyond your limits on public roads, you'll probably be ok with those bikes. Of the two, I'd personally pick the SV650s since people seem to really love the old model and I've only heard good things about the new one. Also, it doesn't have as much plastic to replace or repair in case you drop it. I also think it looks neater but that's just me. I'm sure the Katana is perfectly fine too and it's been around for a good amount of time to make finding replacement parts easy.

I don't know if you've already sat on both but if you can, after you've taken the rider course, sit on both and see which one suits you best. Go with the one that makes you feel good.

On another note, I also recommend going the used route. There's nothing wrong with getting a new bike if you really want one but used bikes save you money and aren't as heartbreaking when the shiny side rubs the asphalt. You also get hurt less by depreciation when you decide to sell and move on to a different bike. But go with your gut and let us know if you ever get one.