What is the time and space complexity of a breadth first and depth first tree traversal?

BFS:

Time complexity is O(|V|), where |V| is the number of nodes. You need to traverse all nodes.
Space complexity is O(|V|) as well – since at worst case you need to hold all vertices in the queue.

DFS:

Time complexity is again O(|V|), you need to traverse all nodes.
Space complexity – depends on the implementation, a recursive implementation can have a O(h) space complexity [worst case], where h is the maximal depth of your tree.
Using an iterative solution with a stack is actually the same as BFS, just using a stack instead of a queue – so you get both O(|V|) time and space complexity.

(*) Note that the space complexity and time complexity is a bit different for a tree than for a general graphs becase you do not need to maintain a visited set for a tree, and |E| = O(|V|), so the |E| factor is actually redundant.

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