It's not obvious to find these numbers in the budget, so we'll have to use a hack. EU permanent staff pays 10.25% of their salaries to the pension fund. Pension contributions are accounted for as revenue, so they are consolidated the section 4 1 0 here. For 2012, pension contributions were at 483mln euros. By means of a simple extrapolation, we can now evaluate the amount paid in salaries to 4.7 bln euros, i.e. 6.5% of the EU budget. With the number of permanent position at 38 482, this gives an average of ~122 000 euros/year salary.
Naturally, the distribution of income is rather unequal at the instititions, with high earners being paid 7 times more that low earners (18 370 vs 2 654 euros/months base salary)
P.S. That's just the permanent positions. There are also contractors and outsourcers.