I used my MIM tele neck and a Squier Strat neck Aug gave me. The body is the MIM tele that came stock with the neck.
A TELE NECK WILL NOT FIT ON A STRAT. A STRAT NECK WILL FIT ON A TELE, BUT THE GAP IS BIG ENOUGH TO PARK A TRUCK IN.
As illustrated here, the gap is pretty huge.
Despite a valiant effort, the pickguard was not able to hide the massive gap.
Difference in shape of the heels.
The tele neck has a thinner heel, I think. When I tried to put the strat neck on the tele, I put a spare string on to test, and the string was against the frets from the first up to the 13th or so, illustrated here (excuse the "give me attention" exacto knife scar from middle school depression):
Different shapes of the necks.
Width at the nut.
Difference in Jedi.