For example,
京都でラーメンを食べたし金閣寺に行ったしお酒を買った。
京都でラーメンを食べたり金閣寺に行ったりお酒を買ったりした。
As far as I know, both are non-exclusive lists and たり isn't in chronological order (don't know about し). Is there any other difference besides that? The one I hear the most in Japan is し, but that might be just because it's Osaka and they have their own way of saying things.
You could say し is cumulative and たり is dispersive.
Repeating …し…し…し… is like combining multiple "... as well as ... as well as ... as well as ...", while …たり…たり…たり… is like lining up "(for example) ... or ... or ... or ...".
As long as the subject is singular, both eventually imply the same person do all the things so that the difference is somewhat obscured, but when you use them with plural subjects:
メンバーはみんなイケメンだし頭がいいし歌がうまいし…
→ They are all good-looking AND smart AND good singers AND... at the same timeメンバーはみんなイケメンだったり頭がよかったり歌がうまかったり…
→ They are all good-looking AND/OR smart AND/OR good singers AND/OR... (a certain member has one or more properties in the list)
The first sentence looks a bit unnatural to me. The last を should be も:
京都でラーメンを食べたし金閣寺に行ったしお酒も買った。
You can optionally replace the first も and the に with も:
京都でラーメンも食べたし金閣寺も行ったしお酒も買った。
In any case, I feel using し is more emphatic, and sounds like "I did various things in Kyoto (including eating ramen, ...)" or "not only ～ but also ～ and also ～". The sentence even almost implies the speaker is satisfied because he had a variety of experience.
Using たり is a more neutral, matter-of-fact expression. "I did ～, ～ and ～."
One function that し has and たり doesn't is provide an explanation or a reason. E.g.
子供じゃあるまいし, 僕に向かってそんな言い方はないだろう.
Don't talk to me like that; I'm not a child, you know!
(from
研究社 新和英中辞典)
(there are more examples but can't think of a good one right now)
However, this applies when it's used alone, not in a list.
