Question: We recently conducted an repeated measures experiment consisting of two conditions. Each condition consistent of three tasks. The tasks are seen as random factors because they are not comparable among themselves. We measured the task completion time.

I have seen something similar, that was evaluated using ANCOVA, but I don't understand why you would use ANCOVA and not a Repeated Measures ANOVA.

Is ANCOVA more suitable due to the fact, that each task is different?

I am really new to Statistics. Maybe somebody can shed some light on that topic for me?

Answer: 
When repeated measurements are taken on subject - either over time or with different conditions - then the within-subject correlation must be accounted for. 

Repeated measures ANOVAs accomplish this by adjusting for the contributions of each individual as fixed effects in the model (a dummy variable for each individual). The ANCOVA approach deals with the inter-dependence by testing the effect of the treatment on the post-measure while adjusting for the initial measurement as a fixed effect. 

However, ANCOVA would only be suitable for Pre vs. Post because the model readily describes the relevant question: "After controlling for initial levels, did the treatment(s) increase or decrease the dependent variable relative to the control group(s)?" The limitation, as discussed in the above threads, is that ANCOVA cannot determine if the dependent variable differed by treatment at baseline. This generalizes poorly to your experimental design.

You are interested in whether the condition affects the outcome across each task (main effect of condition) and, perhaps, whether the effect of the condition varies with the task (interaction). This would be similar to the Pre/Post case in needing to know whether the outcome varied by treatment at baseline and at the end, which ANCOVA cannot determine. Furthermore, it's unclear how the ANCOVA would be specified with more than two tasks. Is the effect of treatment on time in Task A adjusted for Task B and C, or is the outcome Task B and adjusted for A and C? Although I suppose this kind of comparison could arise in some circumstances. 

Thus, ANCOVA is fine for Pre/Post comparison, but repeated measures ANOVA would be more suitable for your design.
I have often read and heard that a) repeated measure ANOVA and b) ANCOVA , the two analyses answer different research questions.

Sometimes, it's not rare seen Researcher disagreeing with the supervisor based on which Analysis would do the right justice to the research question.
I believe that when your research objective is about the mean gain, growth, or change comparing two groups in a pre-post test research (or two groups; of intervention and placebo) the repeated measure ANOVA (time\*subject interaction) really messure this changes. As @moose, it is safe to limit the use of ANCOVA to comparing means of two groups, where you have group(intervention) A, B, C, etc you really need the ANOVA.