On the Air Force side the bonuses are contracted at the time that your aviation service commitment would end, usually about 11-12 years into your career. There is an option for a 5 year extension bonus of $125,000. That money is paid in annual installments of $25,000. There is another option of a 9 year extension bonus of $225,000. This bonus can be taken with 50% ($112,500) in an up-front lump sum at contract signing, and then annual payments of $12,500 for the remainder of the contract term. I am not sure of the Navy bonus terms.
An additional thing to keep in mind is the flight pay. In addition to their regular pay, pilots get aviation pay which is based on years of aviation experience. It starts out at $125/month in UPT training and goes up incrementally to $650/mo. at 6 years of more. There is another jump to $840/mo. at 14 years of aviation experience. This pay is on top of the bonus money discussed above.
My son has found that being a jet (fighter) pilot is a lot more than flying fast in jets. There is so much more time devoted to studying, briefing, planning, etc. than there is actual flying. Also, you will have another job in the squadron (weapons, scheduling, training officer, tower duty, etc.) that will take up as much as, or more time than your flying duties.
To your original question about the chances of a fighter from each Academy, I can't say which has a better chance overall. For actual numbers, the Air Force has 1,970 F or A designated airframes. The Navy has 773 and the Marines have 378 (1,151 between them) so the odds are not too different based solely on numbers. Air Force has more, but as others said above there are not as many USNA grads who are looking to be a pilot.
Stealth_81