Hi, I've only played through twice so far, first time staying with Tallis and second time leaving, so not got enough examples to know if the differences were definitely due to the different choice. However, this is the difference between the two play throughs I experienced
Staying with Tallis: Fenris moaned about us helping the Qunari. Fought that Baron guy, fought some random ghasts, fought the Tal'Vashoth, got the cache of goods. Confronted Duke and on completing battle, got the option to ask Tallis to stay with us (didn't really mean it and not surpised that it was refused), got the option to ask for the scroll but refused by Tallis. Got given jewel instead. Felt insulted that writers forgot why I originally took on this quest.
Leaving Tallis: Fenris commented he was glad she'd gone. Got a pleasant stroll with friends. Anders chatted to me about my father. Got cache of goods. Watched Wyvern fight (helping whichever Wyvern seemed to be getting the worse of it so they both keeled over simultaneously). Had another chat with Anders about how he approved that I had earned my title rather than just inherited it. Got to look over a viewpoint, saw ruins in distance and decided to investigate - stumbled on rendeavouz between Duke and Salit. Saw a cut scene with Tallis in mask impersonating one of his soldiers take scroll from Duke (I'm sure we didn't get this first time round). Fought Duke, didn't get option to ask for scroll but did get option to ask for payment. Ignored this option, got given the jewel anyway. Felt insulted that writers didn't remember why I originally took on this quest.
So essentially there is very little difference between the two, except that without Tallis we seemed a lot happier, had less agro on the way to the ruins and generally had a much more enjoyable spell appreciating the lovely scenery. I may have failed to get the scroll but at least I didn't personally kill any Tal'Vashoth, so it is the option that least benefits Tallis and her rotten Qun. Didn't realise I got more points for doing that - even a small benefit for ditching the b..ehm .. Qun is appreciated.