As a modder of both games I can provide you more specific info which can be interesting for those who consider H2 better than H3. And for those who don't too
1) H3 has a simplified flag color system. Only heroes possess animated multi-colored flags, while the rest are monochrome and static. On the contrary, H2 has all flags multi-colored and thus saturated, with the hero flags being animated as well.
2) H3 has a simplified object passability rules, which has become convenient only starting from In the Wake of Gods modification which allows to change the passability of every object to a custom one.
3) H3 has simplified object shadows with only 2 tones: Deep Shadow and Faint Shadow, while H2 has around 6-7 tones (didn't count precisely), which allows the objects to fit to the background much more neatly and softly. H2 shadows are much less aggressive.
4) H3 has simplified font shadows with only 2 tones: Font Color and Shadow Color. At the same time, H2 uses multi-colored font similar to Amiga IFF fonts, which contain every character as a picture in the game resources. This allows the H2 font fit to the beige background much more; H3 uses only grimdark backgrounds which don't conflict with the standard white font. With that said, H2 still supports the same yellow font coloring as H3. The only thing that H3 is superior at is that H3 contains 3 fonts for various uses instead of 2.
5) H3 has a simplified road/river system in the map editor. H2 allows to make diagonal roads and rivers, which enrich the maps nicely but require some additional skill. However, H3 roads and rivers exclude the possibility to mess up the map because its map editor is more casual and convenient in general.
6) H2 has a specific feature with the arbitrary standing animation of creatures in battle. Thus, Mutant Zombies have their flies moving constantly and Ghosts are levitating dynamically (Phoenixes and Genies have it with a palette shift technique which is present in H3 as well, not sure about Fire Elementals, but I think it's the same case). H3 does not have this feature implemented: its resources contain animations for all creatures, but there is no code responsible to make it moving. Expected to be implemented in Heroes of Might and Magic III: Horn of the Abyss.
7) Same with the negative luck: left unimplemented in H3 while it's present in H2. Already implemented in Heroes of Might and Magic III: Horn of the Abyss and expected in Heroes of Might and Magic III: The Succession Wars Mod.
8) Campaign award system of H2 is lost in H3, but H3 supports hero transfer instead. The award system can be restored by the means of WoG scripting.
9) Campaign alternate mission system which was also lost in H3. An ability to change loyalty from Roland to Archibald and vice versa included.
10) Dynamic castle looks on different terrains, a nice H2 feature, also lost in H3. Will be restored in Heroes of Might and Magic III: The Succession Wars Mod and VCMI engine.
11) Perhaps I missed something.
Anyways, that does not diminish the advantages of H3 over H2 which have been already named a thousand times.
1) H3 has a simplified flag color system. Only heroes possess animated multi-colored flags, while the rest are monochrome and static. On the contrary, H2 has all flags multi-colored and thus saturated, with the hero flags being animated as well.
2) H3 has a simplified object passability rules, which has become convenient only starting from In the Wake of Gods modification which allows to change the passability of every object to a custom one.
3) H3 has simplified object shadows with only 2 tones: Deep Shadow and Faint Shadow, while H2 has around 6-7 tones (didn't count precisely), which allows the objects to fit to the background much more neatly and softly. H2 shadows are much less aggressive.
4) H3 has simplified font shadows with only 2 tones: Font Color and Shadow Color. At the same time, H2 uses multi-colored font similar to Amiga IFF fonts, which contain every character as a picture in the game resources. This allows the H2 font fit to the beige background much more; H3 uses only grimdark backgrounds which don't conflict with the standard white font. With that said, H2 still supports the same yellow font coloring as H3. The only thing that H3 is superior at is that H3 contains 3 fonts for various uses instead of 2.
5) H3 has a simplified road/river system in the map editor. H2 allows to make diagonal roads and rivers, which enrich the maps nicely but require some additional skill. However, H3 roads and rivers exclude the possibility to mess up the map because its map editor is more casual and convenient in general.
6) H2 has a specific feature with the arbitrary standing animation of creatures in battle. Thus, Mutant Zombies have their flies moving constantly and Ghosts are levitating dynamically (Phoenixes and Genies have it with a palette shift technique which is present in H3 as well, not sure about Fire Elementals, but I think it's the same case). H3 does not have this feature implemented: its resources contain animations for all creatures, but there is no code responsible to make it moving. Expected to be implemented in Heroes of Might and Magic III: Horn of the Abyss.
7) Same with the negative luck: left unimplemented in H3 while it's present in H2. Already implemented in Heroes of Might and Magic III: Horn of the Abyss and expected in Heroes of Might and Magic III: The Succession Wars Mod.
8) Campaign award system of H2 is lost in H3, but H3 supports hero transfer instead. The award system can be restored by the means of WoG scripting.
9) Campaign alternate mission system which was also lost in H3. An ability to change loyalty from Roland to Archibald and vice versa included.
10) Dynamic castle looks on different terrains, a nice H2 feature, also lost in H3. Will be restored in Heroes of Might and Magic III: The Succession Wars Mod and VCMI engine.
11) Perhaps I missed something.
Anyways, that does not diminish the advantages of H3 over H2 which have been already named a thousand times.