Ham radio operator here: basically neither will happen because both don't really mean anything.
This is an imperfect analogy, but I think it will set you thinking in the right direction: If someone is blinking a flashlight at you, and you're sitting right next to another person, do both of you see the flashlight at 100% brightness, or do your eyes wrestle for the same light waves?
What does "pick up the signal at 100%" mean? Let's say me and my buddy are talking on our car radios, no repeaters just point-to-point. If we start off in the same parking lot, we can easily hear each other. If we start driving in opposite directions, we'll still hear each other just fine, until one of two things happens: We go on either side of a hill or far enough to be beyond the horizon, and then abruptly stop hearing each other, or the signal will fade in intensity until the background noise is louder.
If we get to that point where the signal is weak but still receivable, increasing output power of the transmitter, or switching to a directional antenna might help. People tend to think antenna gain is some magic that makes the radio louder, but it's not. A high gain antenna does the same thing that cupping your hand behind your ear or around your mouth does; it puts more of the energy that would have gone in different directions in the direction you need.
Without getting too far into antenna theory, I will say that yes having two antennas near each other can cause them to interfere with each other. "Wrestle for the same radio waves" isn't the way I would describe it. Antennas resonate with radio waves, it's like a tuning fork, if you play the note the tuning fork is tuned to, the tuning fork will start to vibrate and emit its own sound. If two antennas are quite close together, this can cause destructive interference. You can use the same principle to construct a high gain antenna; look up how yagi antennas work for more details.