I mentioned a few things in post#2. We can also help you figure that if you provide at least the following info:
1) Room dimensions.
2) Listening distance.
3) Speaker sensitivities in dB/W @ 1 meter, or dB/V @ 1meter and their impedance characteristics.
4) Speaker maximum spl (hopefully manufacturer specifies @1 meter)
5) Speaker configuration. (2.0,2.1,5.1,7.1?)
6) Types of music you listen to.
If your amp has some sort of anti-clipping circuitry built in, you may be losing out on dynamics at higher listening levels. Not a problem if you listen at levels low enough that the amp can take care of say 15 to 25 dB of peak swings freely without inflicting any built in limiting features.
Of the above, 2, 3, and 5 are all that's really needed. 1 won't matter unless the room dimensions dictate the listening position or speakers get within a couple feet of the walls. 4 is interesting, but doesn't impact the basic calculation. 6 relates to crest factor, but doesn't affect the max SPL calculation.
Back to the OP's question, factors 2, 3, and 5 can be plugged into calculations that would land you at your maximum SPL at the listening position at full power. An example would be at a distance of 10', speaker sensitivity at 85dB/1W/m, and 3 speakers (LCR). For your Onkyo at 135 W (more on that in a sec), you land at 101dB SPL max. The biggest factor here is speaker sensitivity, because if you double your power, you change your max SPL by 3dB, but if you find speakers with 95dB/1W/m sensitivity, you've made a 10dB change. In the first example, changing from the AVR to 3 channels of twice the power only lands you at 104dB SPL max. That goes in the right direction, would be slightly audible in the loudest situations, but doesn't help all that much. If you really want louder, you need more efficient speakers.
BTW, a max of 101dB SPL puts your average level for movies at 20dB below that, or 80dB SPL, which is loud, but 5dB below "reference". As source material goes, movies are mixed at a reference level of 85dB SPL with 20dB of headroom, which explosions will often use up. So for undistorted, unclipped sound, we should play movie tracks at 20dB below our max SPL, calibrated with all channels driven with uncorrelated noise. The glitch here is the center channel, which on its own maxes at 96.6dB SPL, 20dB bleow that is 76.6, which is adequate, just barely. Again, upping your power by double changes everything by just 3dB, so if you really want to make a change, you need different speakers. As a rule of thumb, to make a volume change that people perceive as doubling volume, you need to change by 10dB.
If we're talking music, not movies, the peak to average difference can be anywhere from 3dB to 20dB, so it gets pretty hard to predict.
Now, as to the differences between the AVR and separate power amps, one factor is the maximum power with multiple channels driven. Some AVRs can't supply full rated power when all channels are driven equally, but good power amps usually can. Now, that sounds like a big deal, but in practice, nothing we listen to ever drives all channels equally at the same time. So, in the end, the "all channels driven" vs "2 channels driven" specs don't matter much.
As to the presence of clip protection, it's not likely in this case. The maximum short term power is a fraction of a dB more than steady state (135w vs 150w), and the power spec is done at .08% THD. A clip limiter has an attack and release time which affect both the effectiveness as a clip protector, and distortion. To be an effective clip protector it needs to attack and release fairly quickly, which would preclude .08% at full power by quite a ways. Also, clip protection limiters are not frequency selective. Clip protection limiters are not typically found on AVRs, but are much more common in power amps, where there is usually a front panel indicator when they are active.
The above example uses some rather inefficient speakers. Since speaker sensitivity is the key to answering the question, that's really the missing piece.
