To make a match between a radio and a power supply based on the maximum current needed when transmitting is easier to understand, so the question must be asked about the voltage range the radio works well within.
Many times this is not specified as a range like this: 8..16 V (it is used mainly for handies and mobiles), instead, they write in the manuals that the "nominal" voltage is 13.8 V, and you can only guess what range it means exactly.
If the voltage is too high, the radio may go broke. If the voltage is too low, you may have a smaller output power but there can be distortions in the radiated signals as well, and/or the receiver parameters may significantly suffer, and lastly the radio might occasionally break somewhere physically, too...
It comes as a relief that a lot of times the "nominal" 13.8 V means a reasonable range around it, e.g. ±15% (or 10, or may be 5), so if you give the transceiver a voltage inside this range, it will work safely but there is no guarantee for the numbers - at least this is my opinion. 13.5 V is well within even 5 percents, so it should be perfectly suitable.
It is also worth to mention that the duty cycle of a power supply is also important, for how long it may produce its maximum, let's say, 15 A current, e.g. how long you can talk in FM before going to receiving for a while. A lot of time it is not specified, and you can only estimate it for smaller loads, e.g. for 12 A, hi.
In the real life, manufacturers many times speak about 50 percent duty cycle (sending/receiving ratio) for the maximum load without specifying the exact lengths of these periods, or they specify a power supply (or even a radio) that it is capable of "100 % duty cycle", so the equipment can continuously provide its maximum.