For my competition minies, I cast from either a RCBS Hogdon mold with extended base pin or a Rapine Trashcan. The Hogdon is designed for competition and shoots very well in both my Parker Hales. Both of those guns with that minie are sub 2moa when the loose nut at the end of the stock has his poop together. The Trashcan shoots best out of both my 62 Colts, like one ragged hole at 50yds but is a bit unstable at 100. I'm looking for another bullet to counteract that.
For minies to shoot best, use real black powder, good caps, and good lube. Minies must be cast from as pure lead as you can get, wheel weights are a no no. Then they need to be sized to about .001-2 under bore size. Best powder is Swiss followed closely by Old Eynsford (Goex product). My preference in caps are RWS followed by Schutzen. CCI reenactor caps are garbage as is powder marked for "reenactor use". As for lube, I use a couple. The Hogdons respond best to beeswax/lard 50/50. The Trashcans like beeswax/olive oil.
Lee molds- they're priced like that for a reason. I have a couple and do use them on occasion. The only Lee minie I've ever gotten to shoot well was their "target" minie that was a direct copy of the Rapine Trashcan. The Trashcan can't be sized much and the Lee version is very close to the bore size on my Parker Hales. The thing I don't like about that mold is Lee quit making them in 58cal so I'm always on the lookout for a New/Old stock one. I have two, one is pretty used and starting to have issues and I have one new I got off ebay for a backup.