ANCOVA or repeated measures ANOVA? I have 3 groups randomised to intervention A or B or control.  Participants were measured pre and post intervention - should I use repeated measures ANOVA or ANCOVA with the variable measure at time 1 (pre) as the covariate?  Variables are continuous. thanks 
 A: Actually, the post minus pre approach is one that you should always try to avoid. The issue is not about statistics. It is about measurement. When you calculate difference scores, the reliability of the measures become very low. You don't want that.
I prefer ANCOVA if the assumptions are met (and it will in most cases), because the interpretation is easier. The readers of your study will have to look at only the post averages, 3 averages in your case, instead of all 6. If you get an interaction effect, which is expected that you do, you'd have to do a post hoc comparison of that effect. This will give you even more p-values that make reading your paper even harder.
If you want others to cite your study, make it easier to read. 
A: I suspect the best approach would be to get difference scores (i.e., post - pre) for each experimental unit, and then run a simple one-way ANOVA.
A: I would generally say that you need a repeated measures model with group, pre_post, and an interaction term.  What you want to know is whether the post-test score is dependent upon the intervention, so you need to see an interaction.  The meaning of that interaction would depend on actual scores.
A simpler method might be to use a pre_post subtraction score.  That would make the assumption that pre-test differences (significant or otherwise), do not affect the outcome at all, or are not present at all.  Check your groups, and if they are very highly similar then the subtraction score and one-way ANOVA is an easy thing to do.
The ANCOVA is much more like the difference scores or also an ANOVA on the residuals left after removing pre-test.  It's not wrong, and some people prefer it.  I believe I read a paper once recommending it but even they qualified it because pre-test may be correlated with group. In that case interpretation becomes difficult.
Why not run the full ANOVA and the ANCOVA?  If they reach similar conclusions you're safe.  If they reach different conclusions then think much more about what your data mean and maybe come back on here and ask for help at the interpretation stage.
A: ANCOVA gives the same results asymptotically as the contrained repeated measures model (no treatment main effect term). The usual repeated measures model including time, treatment, time*treatment terms assumes the baseline scores are not balanced so its estimator is less efficient. 
Article: 
https://www.researchgate.net/publication/326881265_Analyzing_pre-post_randomized_studies_with_one_post-randomization_score_using_repeated_measures_and_ANCOVA_models
