I second what @Barry has said. The rest is my two cents worth... call it Murphy law if you will :-)
The single number called "gain" doesn't say anything about the particular shape of the radiation diagram. The gain is merely a peak value, at the tallest "lobe". Whether the shape of the radiation pattern "fits your bill", that depends on your "use case" for the antenna.
The radiation pattern can vary wildly with frequency. So does the antenna's impedance at the feed point.
While it would typically be your design goal to tune the antenna such that you get the desired radiation pattern, maximum gain and a perfect impedance match at the nominal working frequency of the (narrowband) antenna, with particular designs you may find out that e.g. the best impedance match can be achieved when the antenna is actually slightly out of tune (off its resonant center frequency) because at its fundamental resonance, its uncompensated impedance is too low for a 50-Ohm feedline. I seem to recall that a quarter-wave stub behaves this way. (In whose case the details of the impedance depends on the availability of a viable "ground plate", or a counterweight "skirt").
In some of my own simulations, I recall that a 3/4-wave resonant stub is a pretty good native match to a 50-Ohm feedline, at resonance - which is only nice if the radiation pattern "like a cup with walls sloping 45 degrees up, a null in the horizontal plane" corresponds to your use case :-) Speak about indoor use, e.g. a WiFi client with AP's mounted in the corners of the ceiling...
Broadband/multiband antennas are a whole different territory... (can of worms). Basically: resonance is a narrow-band phenomenon. A broadband antenna cannot resonate across the band. You can design antennas that resonate at several nominal frequencies... but looking at the practical designs on the market, it's clear that multiband multi-resonant design is a tough discipline.
Antenna "efficiency", especially as a single figure, is quite a dubious category to me. Gain is a volatile mistress, and so is impedance matching. And, considering how many dB of gain and mismatch you can easily collect due to slightly unfavourable circumstances, efficiency as a percentage is a funny idea. Considering that a few dB of actual net gain or attenuation in a signal path means next to nothing, in the parlance of today's typical tuner technology... (AGC range of 50+ dB)
I only have DIY experience with 4nec2 and an old sitemaster, and some very simple radiator types. I'm keeping my fingers crossed for you, to achieve proficiency with advanced antenna designs and design tools.