In my experience, the driving factors in this choice are less about fun and roleplaying, and more about practicality.
Specifically, having players make their own rolls takes some of the pressure off the DM, and gives him some time to think about the consequences of the roll, the probability involved, and generally not be actively doing something for a couple seconds. It spreads the responsibility for maintaining the game (which normally tends to pool on the DM) around the table a bit.
This will vary from system to system and DM to DM, of course. D6 and roll and keep would be nightmares (so... much... counting), while old-school D&D wouldn't be a huge deal. Individual DMs will have varying tolerances as well...
Roleplaying
Regarding your actual question, let's talk about roleplaying. In my opinion, hidden rolls are a useful tool for perception, stealth, and knowledge related checks. Not knowing the result takes a lot of burden off of the player, and frees them to roleplay appropriately. I talk about this a bit in another question. Note that there are some strong dissenting opinions on this... You can find them in the comments and other answers to that question.
For more procedural rolls (attacks, damage, climbing checks, and so on) it doesn't really matter one way of the other. Knowing the roll ahead of time can help you add a bit of description before the DM starts, but this isn't a make or break kind of thing.
Fun
Ah, fun. This is where things get complicated, because everyone has a different idea of what fun is. Roleplaying in particular appeals to different people for very different reasons.
Some people show up to be told a story (that they somewhat participate in). For them, it doesn't really matter if they roll or not as long as they trust the DM to tell a good story. The ups and downs of their character, even the rules of the game themselves, aren't as important as a good narrative. In fact, having to think about numbers and rolls in general only serves to pull them out of the mood.
Some people show up to tell their story. They want to have an active part in the storytelling process, and want power to shape the narrative. They're more likely to want to roll the dice themselves, so that they know that their character isn't being "cheated" for the sake of the DM's story.
Finally, some people show up to play the game. They're more actively interested in the mechanics of the system and their characters. They'll definitely enjoy things more if they can roll their own dice (most of the time), because it lets them see the gears of the system turning in front of them.
Of course, these are broad strokes... Most people will draw from several categories, or jump from category to category over the course of a night.
From what I can gather what you're asking, you want to know the probabilistic difference between rolling 10d10 and 5d20. You've rightly pointed out that each roll has the same maximum and that each has a better chance at rolling their given averages. The averages are different, which you already know. They obviously have different minimums (10 vs 5), and so you want to know precisely how different the rolls are.
Dice rolls are commonly noted as "xdy", where x is the number of dice and y is the number of faces. "d" tells us we're looking at dice and acts as a delimiter.
Any time we look at two dice variations where the product of the number of dice (xdy) and the faces of the dice used (xdy) is equal between the variations, we usually want to know how they differ since the ranges are so similar. In our case, 10d10 versus 5d20 is very similar because 10*10 is equal to 5*20. The following answer can be used as an example for any comparison of dice rolls where x and y on both variations have the same product (2d10 versus 1d20, 2d6 versus 1d12, 3d8 versus 4d6 versus 2d12, etc).
Fewer Dice, More Variation
Using AnyDice.com we can calculate the probability very simply with the commands output 10d10 and output 5d20. And really that's all there is to it. The black line below represents 10d10, and the yellow line represents 5d20.
Generally speaking, when you have a greater number of smaller dice, your rolls are less "swingy". Meaning, there are better odds at rolling the "average". But, you have worse odds at rolling higher numbers. When you use fewer number of greater dice, your rolls are more "swingy", meaning you have less chance to roll the average and more chance to roll the extreme ends of the ranges.
Put another way: Look at this graph, it represents the odds that you will roll at least a given number. You can see in general it's better to roll 10d10 because you have greater odds at hitting a certain number until about 60, then 5d20 gives you better odds at hitting those values, but only slightly.
So with 5d20, you have higher odds at hitting a greater range of values, meaning that if you roll 5d20 often, you'll see more "swingy" results. But with 10d10, the odds are more stacked in the middle, meaning it should feel like you're hitting the "average" or the "middle" results more often.
Another Example
But let's simplify. Lets look at output 2d10 vs output 1d20. Same idea as 10d10 vs 5d20. With 2d10, the odds are much different than 1d20 because there are a greater number of rolls that represent the middle values (11). there's 10-1, 9-2, 8-3, 7-4, 6-5, 5-6, 4-7, 3-8, 2-9, and 1-10 representing 11. 10% of all the combinations are 11. But for higher values (20), there is only 10-10 representing that, which is only 1% of all possibilities. But for a 1d20, there is a 5% chance for every number. So 11 is represented by the same number of faces as 20, or 1.
Similarly, if you wanted to compare 1d100 to 5d20 and 10d10, you would see a flat probability: a 1% chance for each value between 1 and 100.
Conclusion, Final Thoughts
So we can see why certain combinations of damage die are used in RPGs, and more specifically D&D 5e (which you originally asked about). The more dice you can use for a given range, the more you, as a designer, can control the probable outcome of that roll. Whereas some rolls, like loot tables, rely on an equal probability of each result by using only 1 (or very few dice) such as 1d100 rolls. Simply put, if you want to design a system that uses dice, you can control probability more by adding more dice.
Best Answer
Star Wars dice are extremely difficult to analyse statistically and I speak as someone who has taught statistics at a Master's degree level. My congratulations to the people who designed them for that.
You cannot treat success and advantage as though they were independent outcomes because they aren't; both dice have faces with one of each. You also can't add up all the symbols and divide by the number of sides as say that is the chance because this treats .7 successes as a meaningful result which is only reasonable in dice pools with dozens of dice: this never happens. Alternatively, .7 represents the long run average over all possible dice rolls, however, in the long run all humans are dead, what matters is if we avoid death now!
So, what does happen? (All results are /24)
Upgrading gives a 5/24 chance of significant improvement. Reducing you chance of nothing by 1/24, giving 2 success instead. It upgrades single advantage 4/24 times, adding a success 3/24 and another advantage 1/24. In addition it carries that magical triumph symbol, which can change the path of the adventure.
Now additional advantages (and triumphs) are always advantageous (heh) but additional successes are more situational.
In combat each extra success do another wound (yay!); outside of combat you generally need one more success than failure and any left over are wasted, a bit like carrying water through the desert - you have to have enough but too much is just dead weight. To work this out you need to consider the whole dice pool - how many failures will you need to overcome? If it's a lot, a 4/24 chance of an extra one from an upgrade is not to be sneezed at. If success is a cake walk, sneeze away!
As to if light side points are better used for narrative benefits, that is situational on your style of play as well as the dice pool situation. A well prepared group who likes to cover all bases in planning is likely to need them less than a group that takes things on the run.
How valuable a light side point is also depends on their velocity in your particular group. This is largely dictated by the GM's attitude but players have their impact too. A group where points pass back and forth rapidly will value them less "easy come, easy go"; hoarders on both sides of the screen drive the value up. Interestingly, both play styles will tend to have one when they really, really need one: the laissez-faire because they usually have one, the misers because they usually save one.