I will start with the EU. 

For me, I'm not sure which points I would pick from the Eu because I am still collecting and reading through the books, but I do enjoy reading about the Yuuzhan Vong War, Jacen Solo's fall to the dark side as Darth Caedus, and of course the Legacy comics series. I also very much like content from the Old Republic era thanks to the KOTOR and SWTOR games. Very unfortunate that there haven't been more books based on the game's story, a trilogy based on Valkorion or the Eternal Empire would be pretty entertaining in my opinion, or maybe even a prequel story to KOTOR about the Mandalorian wars where we could see Revan, Malak and Meetra Surik fighting  together as Jedi before eventually going on their separate ways. SWTOR also has a lot of cool side characters in the form of companions and certain bosses in the main questline, and I feel like a collection of short stories and novellas about even a few of them would make for a good read in an anthology style. 

(Quick side note: I had originally planned to put snapshots of the companions pages for each class from the SWTOR encyclopedia but that would mean eight separate images, and I'm not sure if anyone wants me to do that right now, so I'm including a poll to ask if anyone would like me to share those, along with my thoughts on the ones that I think would fit the idea I described above, and of course the thoughts of this community.) 

In the canon, I think my favorite moments would mostly come from the Clone Wars series. The ones that come to mind immediately are the Mortis arc from season 3 and the Yoda arc in season 6 (I'm a sucker for that kind of lore, if you haven't already noticed 😉), the Ahsoka arc at the end of season 5 and the Siege of Mandalore from season 7. The last one is easily my favorite of the four, actually felt myself tearing up for the last two episodes. The stuff with Maul leading up to the Siege of Mandalore (like his duel with Sideous, his reunion with Savage Oppress and restoration by Mother Talzin, and his shadow war against both the Jedi and Sith). 

How about you? What are your favorite moments from the canon and the EU? If you aren't very familiar with one or both, that is fine, just pick from what you know. I didn't include any moments from the movies, since the originals and the prequels fit into both timelines, so they seem like they would be automatic options for both, but that is just my logic and you do not need to go by it.