One of the first things to note is the definition of "defeat". To "defeat" the enemy, you must prevent it from attaining its goals. Therefore, it is entirely possible for both sides of a war to be defeated, or both sides to be undefeated.

Sometimes these things are diametrically oppposite. For example, victory for Egypt as originally intended would be "Cross suez canal. Retake far bank. Destroy Israeli forces defending the Suez", while Israeli victory may have been "retain East bank of canal." If one attains the goal, the other side cannot.

However, if the Egyptian goal remains the same, but the Israeli goal was "Survive with full control of Israeli territory", then it would be quite possible for both sides to be undefeated and achieve their goals.

Now, that said, the 1973 fight was a very close-run thing. The Egyptians did, indeed, achieve their initial goals. They crossed the Suez in force far faster than anyone believed possible. Israeli counter-attacks were defeated for two main reasons: Firstly, an under-appreciation of the merits of combined arms. The Armored Corps had turned into the premier branch of the IDF, and armoured brigades were relatively under-equipped with infantry. This proved to be something of a problem when the Israelis charged forward into the teeth of Egyptian anti-tank missile systems. It took several days for the Israelis to figure out that they needed to try again with more infantry.

The other reason was that the Egyptians learned their lesson from the previous war, and brought a LOT of air defense equipment with them. This prevented the IAF from interfering much with the battle between the Egyptian and Israeli armies until the Egyptians changed their goals, moved outside of their protective umbrella, and gave the Israelis the opportunity to counter-attack effectively, which the Israelis did. That changed the Egyptian victory into a significant operational defeat.

Life was a bit different over on the Syrian front. That was quite simply the Syrians sending a LOT of hardware and men at the Israeli defenders, and the Israelis trying to stem the flow. It was a close-run thing, sometimes Israeli tanks would run out of ammunition and hold their place simply in order to scare the opposition. (Part of the reason Merkava was later designed with the rear compartment and hatch). The IAF actually took heavier losses in the Golan than in the Sinai, due to the more limited approach routes and good positioning by the Syrian air defence units.

Fortunately for the Israelis, the limited goals the Egyptians had allowed them to focus everything they could on the Syrians, with only enough forces for a bit to keep an eye on the Egyptians. Once the Syrian threat had been contained, then more resources (and new tactics) could be applied against the Egyptians. Again, though, the question was "What was the Syrian goal?". Was it "The Destruction of Israel?" Or a more limited "Retake the Golan Heights?" The former obviously would be a little more difficult, but the latter would be not an existential threat to Israel (though it would make life far more difficult). Thus, the Israelis wished to keep the Golan heights. In this case, defeat for the Israelis was quite close. Destruction for the Israelis is a far more questionable outcome.

The Israeli Navy had learned significant lessons after getting its arse kicked in 1967, and was dominant in the naval fight in 1973, side-show though it was, but the money for that had been spent previously.

It can be argued that had the Egyptians not had such limited goals in the first place, and conducted a full-scale offensive at the same time as the Syrians, that the Israelis could not hold both fronts at once. Then again, it can also be argued that had the Egyptians continued, all they would have done would be leave their air umbrella sooner, and be defeated sooner.

In any case, the upshot was that the Israelis started a significant upgrade program. The Merkava tank was created specifically for Israeli requirements with the lessons of the 1973 was well in mind. Acquisition of anti-tank missiles increased dramatically (They had none in 1973, no indication that the airlifted TOWs were ever used), and the Air Force undertook some significant modernisation in order to ensure continued survivability in what as now a new high threat environment. Of course, that's just the hardware. You can imagine also what was going on in terms of training dollars.