just some of my thoughts:
Skill system-Nobody has mentioned this yet, but the skill system introduces a whole new level of depth to characters and really help distinguish sword user x from sword user y. The system isn't perfect(like Stg. Joe not being able to use Jongleur), but it was definitely a good idea. the obvious downside to the skill system was that because of it, there were less command runes than previously. But I would take extra character variety and versatility over extra redundant runes(although I missed the Falcon Rune). After pondering this one for a while, I would even say that the overall skill system of 3 is better than in 5, as there is much more variety in the skills and skill levels characters could have. Honestly, the only major improvement 5 made on the system was the ability to transfer skill points to other characters.
Trinity system-although it changes the way the story is laid out compared to the other suikoden's, it also brings out more character development, both for the main characters as well as most of the other stars. You get the opportunity to interact with more characters in different ways. It's interesting to see how characters like Anne react differently to Hugo as opposed to Chris. It's also nice to get a glimpse into the thoughts of the antagonists. My major problem with other suikodens is that you meet and recruit a lot of characters and then never pay much attention to them again. that doesn't happen nearly as much in 3.
I like the plot a lot for suikoden 3. many people didn't like that it moved away from the gathering of the stars emphasis that the other games all have. I think however, that by changing the narrative style, you actually see the point in having all those stars. in all the other games of the suikoden series, there's only a handful of characters that stay plot important for the entire game, and a large number who add very little besides another body. Suikoden 3, I think does the best job of legitimizing the presence of every star, and encourages you to use them. The story itself is nice wonderful, and I think far more reasonable than placing an insane amount of responsibility on one individual, and then also having them casually engaging in all kinds of subplots such as recruiting characters. the other thing that i really like about the plot is that it does a really good job of showing all sides of the story. the enemies aren't just evil(well, maybe Yuber is), the allies aren't all good. Other suikodens have these deep characters too, but I think 3 does the best job of portraying that.
Wars-some people don't like the war system in 3, and certainly it isn't as good as 2's or 5's, but I think it's significantly better than 1's and 4's, which both seemed to be a lot more placeholder than actually interesting on their own part. A big complaint that I've read about 3's system is that it tends to make stupid moves, and gives you very little control. However, I've discovered that training people properly and equipping the right runes does a lot to improving the tides of battle. It just require more planning.
Unwinnable fights: Some people don't like the amount of impossible or near impossible fights. I liked them for two reasons. One is that it rewarded the player's who put in the extra effort. two it added realism to the game. You should lose a few fights along the way. Otherwise, why spend the whole game improving your skill?
Battle system: I liked the concept of the Battle system, It was an interesting way of making the turn-based system more engaging to watch, but it's frustrating watching the computer try to figure how to maneuver characters, and also kinda ridiculous that you can't independently command each character. I did like what it did for area magic, making it possible to hurt your allies within the area of the spell. I was also intrigued by the hidden character types such as berserker, although they didn't seem particularly well used.
Graphics-I don't know why, but i like the graphics of 3 better than 4 or 5's. I think partially it's because I like the side view more than the top-down view, and also I think the cel-shading allowed the character's to look more interesting.
Music-the music is perfectly fine, although because I've played so much and because of the lack of voice acting, I have tended to just mute the game and play other music. That said, I don't mind the lack of voice acting, although I think it could have improved the game much more than it did in 4, where the silent protagonist makes everyone else's presence of voice annoying.
If I was rating the suikodens, 3 would probably be in 3rd behind 2 and 5 and above 1 and 4.