Two's complement is generally simpler to implement in hardware than ones' complement, except for one thing: if one wants a "live" readout of register values using one set of lights for positive numbers and one set for negative numbers (blanking whichever set isn't appropriate) that can be accommodated very cheaply and easy with ones'-complement using one small transistor per bulb and a pair of large transistors to act as master enables for the positive and negative lights. If the states of every register exist as continuously-accessible signals, adding a live readout that shows things in signed format is nice and easy. If a system were to use two's-complement, the values displayed for negative numbers would be off by one, and a significant amount of extra circuitry would be needed for each register's readout to correct it.
In the days when computers had register readouts, using ones'-complement could make the registers easier to read. Two's-complement integer math is better in just about every other way, however.
Incidentally, ones'-complement would make sense with floating-point math if treats 0.1111111111111.... with an unending string of ones as equivalent to 1.00000000. Viewed in that light, the sign bit controls the state not just of all otherwise-unspecified bits to the left of the number, but also the state of bits to the right. ~0 would thus equal ....11111111.0 + 0.11111111....., i.e. -1+1, i.e. zero. Two's-complement representations are asymmetric, but with integer math the asymmetry is consistently one unit. In floating-point math, the two's-complement asymmetry would vary with scale, which is a bit more awkward. Symmetry is more useful with floating point than with integer math, and thus ones'-complement would be advantageous there compared with two's-complement. Sign magnitude also works (and is what many systems actually use) but ones'-complement could work essentially as well.