Played both when they came out. They are very different games and very much reflect the era they were written in. Galaxies was released in 2003 and SWTOR in 2011. It's a bit like trying to compare apples and oranges as they are very different games despite being in the Star Wars Universe.
Star Wars Galaxies comes in two flavours currently: Pre-New Game Engine (NGE) servers and NGE servers. Even in Pre-NGE servers there are some differences around the Combat Upgrade version or lack of it in there build. Your would need to do a bit of research as to your preference of version and features or lack of it. Main difference between pre and post NGE servers is the skill/class system. Pre- NGE has a mix and max skills based system and NGE has a fixed/limited set of classes.
Crafting and resource collection are amazing in either version of Galaxies. UI is well, very different from modern standards and the key binds are interesting. Graphics are dated. Quest system is limited as Galaxies is a sandbox game where you can live the life of a moisture farmer if you want. The housing system is amazing as well for it's time.
Galaxies had a lot of major additions to its game play over it's development life so an NGE server has a lot of game play complexity. Economy is mostly broken due to inflation etc on the two different servers I have played on. No idea on the state of other servers as there a quite a few of them around.
en.wikipedia.org
SWTOR is a much more modern game compared to Galaxies. It has a fixed class based system and classes have some restrictions around which faction your choose. Want to use force lighting on your friends and enemies then you must embrace the dark side

. If you like a good rpg story and quest system then SWTOR has it in spades. Need a companion to care about or ignore then SWTOR has it. I was not keen on the crafting system in SWTOR but it has one. No idea about the economy as I don't currently play. I do own a bit of the DLC but the Aussie servers shut down a long time ago and I had to migrate to a US west coast servers and enjoy the lag. When they removed them and your only choice was US east coast servers I gave up.
I could keep typing but I would need more info about your gaming interests ?
Personal I started 3 times on different servers with Galaxies as I was not used to sandbox games and that was in its hay day of 26+ servers. Max level master architect (crafter), combat medic/doctor/tka and post NGE a commando, trader (domestic goods) and entertainer.
SWTOR I just jumped in on the unofficial aussie US server and was away. I have played 3 different characters to max level on the dark side and one on the republic side. Loved the story for each of them.