Wow!!!! Some crap being spread about here lol....
A few pointers that aren't an attempt at diagnosing your 'possible' fault....
1, Later Sony units are simply awful with regards output quality....
2, Any positive EQ adjustment is likely to induce 'clip'....
3, Any speaker incorrectly mounted will suffer a drop in output quality....
4, Any speaker simply screwed into a stock, unmodified door will not perform at its best....
5, 90% of after market speakers are designed to be used in conjunction with a sub....They simply aren't designed to reproduce lower frequencies....
6, You should avoid comparing how different cars sound, each will have its own individual acoustic properties & as such should be treated differently....
7, Any source unit or amplification stage will only be as good as its power supply....
A few quotes to remember....
If it's just the amp in the head unit, try switching off all the loudness and tone controls and start with everything flat response. If it sound crap to begin with then simply adding bass probably won't help.
The only fair test of a Head Units quality....
Best to have a 200 watt amp running a 50 watt rated pair of speakers than a 50 watt amp runnig a 200 watt pair of speakers. (trust me in this I am a qualified electronics audio service technician. I can explain in more detail if your interested. If you do have a seperate amp then make sure its correctly set up.
To gain the best from your speakers the above is true....BUT, by using a less powerful amp the only loss would be output volume, (assuming both amps are correctly set up)....After all, playing at lower volume doesn't promote speaker damage....
LF (low frequency units or subs) can be any where in the car usually the boot, as these are monoral.
Subs can be mounted anywhere due to the frequencies they are reproducing....Sub frequencies are omnidirectional so stereo or mono has no bearing what so ever....
Finally a 1 farad cap suppling the amp will aid to give a crisper punchier sound by improving the current draw to it.
Sorry mate, it simply won't....A cap would still be seen as a load on your charge circuit in the same manner as a second battery would....The difference being a second battery actually has a reserve capacity, which the cap doesn't....A cap could be used in this manner if your goal is ultimately pure sound quality, but in this scenario the cap would simply stabilise the power supply voltage, (create a steady voltage with minimal voltage peaks & dips), to improve overall output quality....
A 1 Farad cap would be better used up front on the Head Units power supply....This would yield a much more stable pre-out voltage....
Car audio is swings & round a bouts mate....What affects the charge circuit will also affect the Head Unit....A dip in voltage due to a big bass hit, will induce the same dip in the Head Units power supply, which will also affect pre-out voltage, which in effect lowers the amplifiers output volume....
Due to power supply differences you simply can't compare home audio to car audio....There are few similarities....
If you should be close to Derby anytime soon then contact me & I will arrange to meet with you....My Becker is currently waiting for my new car & would take only seconds to fit into yours....This would give a clear indication as to where your problem lies....