In my opinion, the finishing of all three is great, and it probably shouldn't be the deciding factor in choosing between the brands. I think there's less of a gap between these three than there is between Patek/Laurent Ferrier/Voutilainen. Finishing can also vary a bit depending on the models for each brand as well. A few thoughts on each brand:
Most including myself would consider L&H the best finished of the three on average. The polishing of the teeth on the crown/ratchet wheel, the bevels on the gear spokes, etc. and the general finishings as a whole look a bit above what you would probably get on a comparable MG or Lange. The diamond end-stones on the balance wheels are also a really nice touch. The Georg is undoubtedly one of the best finished time-only watches you can get at any price level.
MG's finishing quality is very good as well. It's worth noting that they used to sell "pure" models with less finishing (I think they can still be ordered directly but I'm not 100% sure), so they can be said to have the lowest level of finishing of the three from that perspective. The main criticism of the finishing on MG's watches is that the anglage looks simpler than what you would get from both Lange or L&H. However, they are specifically known for having some of the best watch hands of any brand. Something I'll note that I think gets less attention than it should: MGs have a lot of engraving, which usually includes two fully engraved cocks, along with engraved text on the 3/4 quarter plate.
I think Lange could arguably be said to have better finishing than the other two at the high end like in their Handwerkskunst models, and they are definitely stronger in complications. The anglage is quite good, especially on watches like the Datograph where they use parts with odd shapes and interior angles. On the more entry-level pieces, my criticism would be that while the finishing quality is good, there's not a lot of it. For example, the balance cocks can be small with relatively little engraving, and the crown/ratchet wheels (when they are exposed) are not as elaborately finished as L&H's or MG's.