if you are going to play straight constant sine tones instead of music, then i would say alt first. here's an example: i just did an install in a honda civic, with a small factory alt and they have small batt's too. put in a true 1000 watt amp to the subs and a drycell batt. (he has another amp on his highs too) and upgraded some + and - wires. guess what, with the car IDLING, the voltage only dips to 12.8 V on the heavy bass notes. that is with the system running full bore. the light dimming is minimal. this is a daily driver not meant for competition. he has 2 12's, putting up 142 db's on the TL (= 149 on an AC mic) on the dash, out of a simple common trunk install. so it isn't sissy equip. so spend $150 on a batt, or $3-600 for an alt. you will need the batt any way, so do it first. it might solve the prob, it might not. but if it does, it just saved you all that alt money. that is one reason i say batt first, then alt.
like mentioned before, the problems of normal batteries. dry cells have far less internal resistance. only the term transient response is for speakers, not the charge and discharge capability/speed of a battery or capacitor. i've been playing with drycells for a few years now. recently more competitors are using them, and more people on the streets are starting to switch over too. the xstatic battery is a real hot ticket, but at $900.........not many want to fork that out.
i have both dry cells and ohio gen ho alt.

 

You can get HO alt's for $200-300, or spend $150-180 on a dry cell that will do nothing? I paid $240 for my custom alt shipped. "Transient response" can be used for anything

 

ok, let me say i have never seen transient response used for anything other than referring to a speaker. not in any of my technical studies in the audio industry, nor in my electrical and electronics college classes i had.
here's what i have found in all my years of being involved in the car audio industry.
1- replace the + and - cables under the hood first. it is the cheapest and i have seen cases where that alone cures the dimming light problem. the alt to batt, batt to body, frame, and engine. in the event you go to an ho alt, you will need to anyway. and don't skimp on the neg leads, they are the most important. as electricity flows from the neg to the pos.
2- upgrade that battery. deep cycles are good, but dry cells are superior in ALL aspects. read up......
http://www.odysseyfactory.com/
back when optima's first came out, i remember the difference in bass when i upgraded my stock battery to an optima. it was deeper and more solid. a good battery will make a difference. now with drycells, i feel they are supeior to optimas. on a high amperage charge back, optimas tend to get "dried out" and take a dump. and add a battery before a cap. a second batt or even just swapping to a superior batt, will make 100 times the difference than spending equal $ in caps. caps are known for discharging and charging faster than lead acid batteries. but if you have a batt that is fast as well, it is superior to caps.
3- then go to the alt. and don't always look at price. quality and true output come with a cost. irragi alts seem to be holding up decently and are less than ohio generator alts. but still, the 280 amp alt from irragi is still around $300.
take it how you want to. 16 years in car audio, this is the order i have found to be the most effective and proper in electrical system upgrades. replace from the weakest link forward. different strokes for different folks.

 

lol, i think you are missing what i am saying. i am in fact saying start with the simple, that i don't think a cap is needed. i think 140 amp alt will work just fine. hence the example i gave of the civic with it's dinky alternator pushing a 1000 watt amp with minimal issues. and if you've ever seen their battery, it's about the size of a motorcycle battery. so that is why it got upgraded. ohms law is very important, but it is just the beginning off things to take into consideration.

 

I agree to upgrading the wire first, it is needed for a HO Alt anyways. The battery makes no difference, dry cell and deep cycles will only make it so you can run the system longer without it being charged. Everyone has their own oponions and experences.

 

i havent had any issues so far on the hwy my my voltage reads right at 13 so i think im good