I don't think that they shoulddamage your gun, but i don't have alot of experience with Browning shotguns.

I have a buddy that tried shooting an 11-87 with the rifled choke tube with poor results. It seemed what ever slug he used the results were the same. One day while I was with him when he was trying to sight it in I noticed his slugs were tumbling and hitting the target sideways, I don't think that choke tube was enough to stabilize the slugs. He now uses the old federal rifled slugs with good results.

As far as one type of slug working better than another, that is going to differ from one gun to the next. The only way to really tell is to try them out for yourself and that can get knid of spendy. I do think the sabot slugs are worth the money, I shoot an 11-87 with a fully rifled barrel w/a contilever mount and nikon 2-7x32 on top of it. I shoot the Hornady sst's out of it, with awesome results.I made my longest shot with a shotgun with this setup this fall, I shot a coyote at 194 yards- I had witnesses so that even makes it better.

Hope this helps
Tom