I couldn't imagine playing Millenium with anything other than invisible encounters.

There are some games where visible encounters are essential, such as
- Dreamscape (In this game of limited resources, every battle has a cost. I don't think the resource management puzzle would even be possible if you couldn't choose when to take a power up and when to fight.)
- Aveyond 3 : The Lost Orb (In the beginning our protagonist has no money, and needs to run through the woods finding gold, dodging monsters that are too strong to fight yet. Can't dodge monsters if you can't see them.)
- Vastar (Played this recently. Most areas have monsters with a wide range of difficulty, and the player needs to choose which ones to fight and which ones to dodge.)
However... There is nothing that puts me to sleep faster than going back and forth and back and forth between two maps, killing the same groups of visible monsters over and over and over again to level up my characters.
In games like Millenium, where building levels is important, I like invisible encounters better, especially with adjustable encounter frequency. Marine's Hide or Fight skill is brilliant! When playing Millenium, I can turn up the encounter frequency, and go slowly through a map, clicking on everything to find secret rooms and other hidden stuff. When I'm done, my characters will be all leveled up, and I'll have been rewarded with all the hidden goodies I found. I find this much more fun.