The difference between 15 watts and 80 watts is only 3.5 dB. Not insignificant, but not huge, either. In terms of "absolute loudness", the difference is small. As a rule of thumb, a 3 dB change in
loudness is clearly but subtly audible by most people (some "golden ears" can hear far less change in sound levels... but that is not
most folks). For comparison a sound that is
twice as loud as another represents a change of 10 dB. The sensitivity of our hearing is non-linear.
The "300 watts" number ascribed to the loudspeakers is meaningless (it represents the nominal power handling capability of the speakers... but without knowing a
measurement standard for that value, it is
literally meaningless). The important parameter is the
sensitivity of your loudspeakers. That will detetemine how loud they'll play with a given amount of input power. My guess is they're pretty sensitive -- in which case, they should be OK. The suitability of the amplifier for those speakers will also depend on the kind of music you like, how loud you like to listen, and the size (and acoustic environment) of your room.But this is strictly a
quantitative assessment. The
qualitative assessment (
how it sounds to you) is going to depend on -- you.
You may or may not like the
quality of the sound from those loudspeakers -- with
either of the receivers/amplifiers in question.
EDIT:
IF this is the CS-707 to which you refer, they should be
plenty sensitive for the little SX-434 (if the specifications are
any where near accurate). According to this, they're capable of 98 dB of sound pressure level (SPL) output at a distance of 1 meter given input power of 1 watt (which is 2.83 volts into 8 ohms).
https://www.hifiengine.com/manual_library/pioneer/cs-707.shtml