It seems like the trend in roleplaying has been toward a nearly universal use of unified mechanics (having a basic rule that repeats throughout the game such as d20+modifier). The first time I became conscious of this concept was when TSR released Alternity in the late 90s (though it wasn't the first game to do this and I had certainly played unified systems without realizing it prior to this). One of their marketing claims was that they built the game around a core mechanic. Whether they succeeded or not I can't say, because I never played Alternity, but the marketing campaign created a strong impression on me. When Dungeons and Dragons 3rd Edition came out a year or later it was clear they built the game around the d20 roll (though I have no idea whether Alternity impacted WOTC design of 3E). This was a major change for D&D because the previous edition had a number of disparate mechanics throughout. Yes d20 wasn't a pure universal mechanic like some games have today, but at the time it was a huge break from 2nd Edition. I think it is fair to say that the d20 system helped make the unified mechanic a feature of most modern RPGs because of its popularity. It just became the default assumption that unified was the way to go.
Unified mechanics are good. I like them so much that our own games feature a unified dice pool mechanic (with a handful of edge cases). The benefit of a unified mechanic is you don't have to stop and look things up all the time because you pretty much know how the system handles any situation requiring a roll. So count me as a fan of unified systems.
At the same time, it is kind of a shame that non-unified approaches have fallen into disuse. It is a little like when movie makers adopt a single aesthetic or formula for a decade. Even if the aesthetic is breathtaking and the formula is tight, the brain craves a little variety once in a while. It rebels against the style's omnipresence.
I hadn't given non-unified systems much thought until I ran an AD&D 2E campaign last Winter and realized they have their advantages. The game was set in the Ravenloft Setting and I noticed a number of things when running it. A lot of my observations had more to do with the different assumptions of 3E and 2E, but some of them relate to the subject at hand.
One of the problems with a unified system is it forces you to apply a single solution to every problem. What works for attack rolls may not be the optimal choice for damage or skill tests in your game. Even in unified systems there is rarely pure unity because of this issue. Take d20 for example, yes you apply the d20+modifier to skills and attack rolls, but not damage. Imagine if they had attempted to make damage a d20 roll. It certainly could be done, but not without affecting other parts of the game like hit points. By assigning weapon damages to different dice the designers retained more control over damage. It was something they didn't want to compromise in pursuit of the core mechanic.
When I ran 2E, the first thing I noticed (or remembered since it was the system I cut my teeth on) was there was pretty much a different kind for of roll for any action. Non-Weapon Proficiencies were handled by an Attribute Check (roll under your score) on a d20. Attacks were handled by THAC0 using a d20. But many of the rolls used different dice entirely. Initiative was a d10 with lowest results going first. Thief skills were a percentile roll. Some rolls called favored the higher number, some the lower number. The system truly was all over the place and this did make things a little trickier to master. However I found some things worked better than in 3E.
The Non-Weapon proficiency roll was more contained than the d20 skill roll. Sometimes in d20 the modifiers get a little crazy. But since you roll under your attribute for NWP in 2E, that kept things well under control. The d10 roll for initiative made things easier for the GM (perhaps not for players) because it was much easier for me to keep track of a range of 1-10 possible initiative scores than 1-20+.
It also allowed actions to feel different from each other. That is a vague claim but it was my experience going back to 2E. Making a thief skill roll felt like a substantially different experience than making a THAC0 roll. There is something to be said for the feel a mechanic produces. And I think in this case I started to enjoy rolling 1d10 for Initiative.
At the end of the day I still prefer unified mechanics. Ultimately you can still fine tune the probabilities however you like using a single system. But there is an appeal to games with lots of fiddly bits that do different things very well (and yes I realize there is a strong argument 2E doesn't achieve this).