Like Englishal, if I am joining the circuit and I am approaching from the deadside, I will call descending deadside as I approach the field and cross the numbers at circuit height. This is still a deadside descent and join, and all that is needed is a good lookout and listening to the R/T for spacing (as with any join). It is easier and safer than doing a "360" over the airfield. There is no reason to be upwind of the numbers if done correctly, as all that is missing is the turn over the airfield during the descent.
Whichever direction we join from there is always the chance that two aircraft can meet over the numbers. When this looks like it may happen I will do a more gentle turn to let the other aircraft go ahead or position accordingly. Sometimes I will make a radio call to state my intentions or to ask what theirs are.
Why was the first aircraft lower ? Your initial post suggests you were at the correct circuit height having completed your turn so he must have been below circuit height. A radio call from him to clarify his intentions would have been helpful
As for the second case, there is no excuse for such a join.