Is CT-Art better for tactic training than chesstempo tactics? What are some major differences of doing tactics training using chesstempo or CT-Art?
The answer to the title question is "No, they're both excellent for tactics training and are good at different things."

Chess Tempo:


problems are a random selection of positions taken from actual games (chosen by computer to be good chess problems)
over 100,000 problems and growing
problems are served to you based on your rating
no extra didactic material, but you can read other users' comments and discussions on the problems, and look at computer-evaluated variations
free for basic usage, costs money for some extra features
online only (it's a website)


CT-ART:


a specifically designed course with many composed problems (and some based on real games), so it is explicitly trying to teach you certain subjects
a fixed number of problems (thousands)
you just go through the courses in order
occasional didactic feedback asking you to demonstrate simpler patterns that can be put together to form the desired combinations, but no English discussion
costs money
can be used offline (it's an app)