There should be some difference in efficiency, on the basis that the vertical portion of an inverted-L is "pure radiator", whereas the horizontal portion functions partially as a capacity hat (but not entirely — it also radiates). You can see this in the fact that an inverted-L has a lower feedpoint impedance than a quarter-wave built for the same band. However, the difference might not be much in your case.
The closest thing I can find to a direct treatment of your question is in W4RNL's Straightening out the inverted-L. On pages 15-18 of the PDF he considers an inverted-L for 80 meters of 69' total wire length (approximately a half-size version of your antenna) over modest radials and average ground. He doesn't discuss the quarter-wave vertical, but what he does do is look at three variants of the inverted-L: one with the vertical and horizontal segments both 34.5' ("balanced"), one with 23' vertical and 46' horizontal ("short"), and one with 46' vertical and 23' horizontal ("tall"). As expected there are differences in pattern, especially when the antenna is used on higher bands, but focusing just on the design band, he comes up with these numbers:
Short: -2.1dBi peak gain at 33° elevation, 31+j7 ohms Z
Balanced: -1.5dBi peak gain at 29° elevation, 40+j7 ohms Z
Tall: -1.4dBi peak gain at 26° elevation, 49+j10 ohms Z
Which suggests that the efficiency effect is definitely there, but that the "balanced" configuration has already reached a point of diminishing returns. If two-thirds vertical is only 0.1dB better than one-half vertical, then all-vertical is probably only 0.1dB better than two-thirds vertical. The radials in Cebik's model are pretty marginal, so maybe an antenna over a better radial field would benefit more from the additional height — but if you don't already have great radials, then you might find more payoff there.
All that said, if you want to lower your pattern, then additional height will do that for you.