I'm having a situation at work where my boss (who I rarely work with) is telling me to do a piece of work one way, but a senior team member (who I work with often) is telling me to do it another way. If I listen to my Boss it is going to annoy my team member and I work with them often so I don't want this, and obviously I don't want to anger my boss, so who do I listen to?
Can't you find a third option and speak to your boss stating your senior team member has told you to do it another way and he thinks it's a better way because of X, Y and Z? I don't know your exact situation but in my experience the senior team members often know the systems better and can find better solutions than the bosses.
It may be the opposite in this case, that the boss knows better, in which case when you present the above to your boss he may give you X, Y and Z reasons why you should be doing it his way, which you can explain to the senior team member. It may be that the senior team member doesn't have the full picture.
Either way, dialogue and communication between the three of you seems to be your solution.
I agree with Styphon's answer, that what really is needed is an increase in communication. Unfortunately, you are not the primary party -- the Senior team member needs to discuss this with the Boss:
- The Senior team member may posses detailed knowledge that the Boss does not have the benefit of, which potentially invalidates the direction the Boss is giving.
- The Boss may posses strategic knowledge that the Senior team member does not have the benefit of, which potentially supersedes the detailed concerns.
However it seems these two are not communicating effectively. Thus your difficulty, since you lack any explicit authority to make them discuss the situation.
Your highest priority at this point is to follow your Boss's orders. The Boss will most likely want some sort of immediate action, but what you can do is express concern to the Boss that the directions as you understand them do not align well with your understanding of what the more experienced team members are saying. Ask for a meeting with all parties (as Styphon suggests) -- if possible before you take action, or if a delay is unacceptable, request a modified (e.g. partial) action immediately which everyone is OK with.