Personally, I've always used Random Events for all minor encounters, because when I've used Evented Encounters, they require a few things:
- You need some "Monster Encounter" sprites. This is fairly easy since the RTP provides a few and I'm sure there are many more. When I did a sci-fi based game, I couldn't find any good monster sprites though.
- If you want each Monster to have a unique Sprite, it gets more painful (more Sprites required). But, if you do what Zelda 2 does --- have just 2 Sprites, one for "weak" and one for "hard" encounters, it can work quite well.
- You need to do some Event management if you want the monsters to respawn while the player is still on the map, such as "Make Event vanish for X cycles, then re-appear" This isn't too difficult.
- Too many moving Events can cause a game slowdown, particularly if you have other moving Events onscreen. This limits the number of enemy encounters you can have. To be fair, it's NEVER a good idea to utterly swamp the player with encounters.
I ALWAYS use the Evented Encounters for major, specialized encounters like boss battles, significant cutscenes and the likes. Although I'm probably going to try for Evented encounters in my current project, just to see how it goes.
Even when I use Random Encounters, I avoid rare Random Encounters, because they either mean the player gets the exquisite thrill of grinding in an area to find the rare enemy, or the player might get utterly curbstomped by a very hard rare encounter. I did once have a Vorpal Bunny rare encounter, but made it fair by having it do nothing for 1 turn (in the Monty Python reference, it did, until it was attacked). This let the player escape safely.
In general, I want my rare encounters to be, well, predictable and fair. Either case of Random Encounter-spawned rare encounters makes the player at the mercy of the Random Number Gods.
One huge pro of Evented Encounters is the player feels s/he has some control over WHEN to encounter (or not) the monsters. It works quite well in, say, Chrono Trigger, where the monsters are at defined locations on the map.
If I did use Evented Encounters, I would definitely use very different Sprites to indicate easier and harder encounters, as well as the rare/boss encounters.
On the other hand, Random Encounters' advantage is they by definition surprise the player and keep the player guessing a bit. And they are easier to manage than Evented encounters. Final Fantasy IV did this quite well, and the RE's set a tense tone going through the maps because you never knew exactly when you'd be attacked.
The goal is the player should never feel s/he has no control over significant portions of the game. So all encounters, whether Event based or Random Encounters, should always be fair. So, if you do REs, make sure the encounter frequency is NOT set too high, or it will frustrate the player.
I personally think rare encounters should almost NEVER be dropped on the player out of nowhere, out of fairness.
But as others have pointed out, you can VERY easily make Event based encounters random but fair. Say the "Lesser" Event sets a random number from 1 to 10. Then you can use a series of Conditional checks and make the encounter have different probabilities --- say a 50% chance for a Slime, a 40% chance for a Bat and a 10% chance for a Kobold.
I think non-rare and non-boss Event encounters should mix things up a bit, as long as they stay within the same monster difficulty. And I think minor critter Events should respawn after some delay.