From what I've read, they work slightly differently. Flax oil contains alpha-linolenic acid (ALA) which your body can then turn into the fatty acids your body needs-- inluding EPA and DHA, which a good quality fish oil provides raw in relatively large quantities.
For weightlifting I'm assuming you're taking fish oil for the anti-inflammatory properties of the EPA/DHA, which require that your body convert the ALA in flax oil into that first-- and that doesn't always happen (if you have health concerns, or if your body needs a different fatty acid other than EPA/DHA), and when it does happen it doesn't occur at a rate high enough that would make flax oil comparable to fish oil's benefit.
If your overall goal is to get anti-inflammatory and long term health benefit from EPA/DHA then I'd definitely take fish oil, or eat plenty of salmon and round out your diet with flax oil or other ALA sources like walnuts/hemp to make up any deficiency.
In fact, I've been considering adding a small amount of flax oil/flaxseed to my diet in addition to EPA/DHA from fish oil, to make sure I get the other fatty acids I might be lacking in my diet... but I have to do some research on that first.
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