The images are different but they end up meaning the same thing. The difference is seen better if you write them in active rather than passive voice: #1) They obsess over the thought of revenge. #2) The thought of revenge consumes them. The difference is that #1 sees "them" as the cause whereas #2 sees the "thoughts" as the cause.

‘Obsession’ has the idea of thought built in. For example, you can just say ‘obsessed by revenge’. ‘Consumed’ means used up in all senses, not just your mental energy. To say that you are ‘consumed by a thought’ suggests that it forces you to act in a way that has consequences beyond monopolizing your mind.

Yep, they mean the same thing. Obsessed versus consumed even carries a similar degree of severity, etc. Maybe, 'consumed by/with' could be viewed as slightly stronger, but they basically have the same meaning.