Having played both games extensively, I feel the most interesting thing to analyze about in which parts of the game are randomized, and how that randomization impacts gameplay. Let me pick 2 examples.

In Diablo 2, areas were randomized internally but externally consistent: the individual makeup of areas would be different every game, but the connections between different areas would remain the same.[1] This means that repeatedly exploring the same area remains entertaining for a relatively long time in Diablo 2. This is important, because as you say, items have a higher chance of dropping from certain monsters than from others. If you "have to" keep farming the same area over and over, it helps prevent boredom if that map is different every time.

In Diablo 3, the internal layout for each outdoor area is always the same, and even indoor areas are relatively static, compared to Diablo 2's. After a while, you know the best way to maximize efficiency, which encourages people to repeatedly farm one area, but this is a double edged sword: once you know what the most profitable way of playing the game is, playing any other is much less attractive. This actually reduces the range of (rational) possible actions in the game, inducing boredom more quickly. In addition, some of the best areas to farm in Diablo 3 are the dungeons. These are (smaller and optional) sub-levels within areas. Each area had fixed dungeons in Diablo 2. In Diablo 3 areas can often spawn 5 or 6 different special events, while it has only 2 or 3 (fixed, just like the areas themselves) spots for such events. This adds another layer of randomization: you need to be lucky twice: once to find the dungeon and once again to find the item in the dungeon.[2]

Something else that changed between Diablo 2 and 3 is the way item affixes are randomized. In both games, magical items can spawn with certain properties, and those properties have stat ranges. You might find a Short Sword with the Red prefix, giving +1 or +2 damage. In Diablo 2, the best items (Uniques, Sets and Runewords) had fixed affixes with random stat ranges: you might find a Tyrael's Might with anything between +20 Str and +30 Str (in addition to have a dozen other affixes), but that it would get a significant +Str roll was guaranteed. Even the worst Tyrael's Might was a great find. Relatively casual players would be happy with any stat rolls, while true Diablo 2 addicts would make do with nothing less than a +30 roll. Such a perfect roll could (and still can) increase the value of an item by a factor of 10 to 1000+,[3] even if the objective difference between a random roll and a perfect roll is fairly small in the grand scheme of things.

In Diablo 3, this was thrown out the window. Legendary and Set items get some fixed affixes, but even if you got the best item in the game and perfect rolls on the fixed affixes, you still need 1-3 other affixes to get a genuinely good item. In addition, the stat ranges were much wider. Immortal King's Tribal Binding could get +30 or +200 Str, and with the right random affix, all the way to +300 Str.[4] This makes the relation between gear cost and power fairly linear. You might have to find half a dozen Tribal Bindings before you got one worth using. In addition to finding the dungeon, and then the item, you also need to get good affixes on the item, then get good rolls on your affixes. Finally, in some slots, the best items in the game were not Legendaries, with their half-random setup, but Rares, with fully random affixes, which instead of 1-3 good affixes, need 5 or 6. It is no wonder then that players were unable to find their own items, and were forced to turn to an auction house, where they were primarily supplied by bots and gold farmers (unknowingly, but still).

Blizzard tried to address some of these issues in the Reaper of Souls expansion. Here's a few examples relating to the above points:

* Enchanting was added: allows you to replace one of each item's affixes with a different one (only one affix per item, but you can repeatedly change the same affix until you get one you like), reducing the impact of random affixes.

* Rifts were introduced: random dungeons with random monsters and a random boss at the end, which are generally slightly more efficient than just farming normal areas.

* The auction house was removed, reducing the impact of bots and farmers, allowing an increase in the drop rate. Trading in general was removed as well, making it impossible to turn to third-party trading sites (as was common in Diablo 2).

* The stat ranges on affixes were reduced, lessening the dependence on highly random items. Many Legendary items got unique Legendary-only affixes that (when combined in clever ways) make them far better than fully random Rare items.

Overall, this has significantly improved the game, but having played Diablo 2, Diablo 3 and Diablo 3 after the Reaper of Souls expansion, I can't help but feel like these are in the end just patches on a fundamentally flawed design, and that some of those patches actively prevent it from becoming better. Diablo 2, on release, was a bad implementation of a great design. This allowed it to be improved over the course of almost a decade (sporadically by modern standards, but impressive at the time). Diablo 3, on release, was a mediocre implementation of a bad design. Blizzard improved the implementation (at significant cost, to the point of forcing them to postpone the expansion), and details of the design, but it is still only a good implementation of a mediocre design, and improving it much further strikes me as uneconomical, to put it mildly.

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[1] For example: http://classic.battle.net/diablo2exp/maps/act1.shtml

[2] It's worth pointing out the two different types of randomization in games. One is the type the player can influence, like which area to farm and whether to play solo or in groups. The other is forced upon players, like what affixes your drops have or whether a dungeon spawns in a given area. Players tolerate the latter to much higher degree than the former.

[3] Filled with jargon, but: http://forums.d2jsp.org/topic.php?t=59979863&f=52. Look at Hellfire Torches for a typical desireable item, and Black Hades for an extreme example.

[4] These are the post-expansion stats, but it illustrates the principle, which is much reduced, but still very much alive: https://us.battle.net/d3/en/item/immortal-kings-tribal-bindi....