Traffic is lousy during peak times (especially afternoon rush hour) and I definitely wouldn't want to make a lot of east-west trips during that time. But most of the time, traffic is manageable, and I feel that Taipei taxi drivers very rarely attempt to take advantage of their passengers.

Typically, it will take longer to get an Uber than flag down a taxi.

Location is always dependent on personal preference (maybe the MO will be appealing to those who like traveling to foreign countries but have a Gordon Biersch, Ruth's Chris, and IKEA nearby - who knows). But yes, to me the Shangri-La location is better. It's on top of a mall which is good for convenient shopping/restaurants and is also near Tonghua night market, which is my personal favorite of Taipei's night markets. IMO the nearby restaurants are more interesting as well (including an absolute gem in Ephernité, whose exec chef used to work at L'astrance and has a farm-to-table focus). The MRT is also accessible although via the least efficient/convenient Brown Line, so probably still a property that guests will want to take taxis from frequently.