this came to me, does the lure and line (size) have same effect for catching more and bigger fish ?

for instance, a medium size floating minnow with 14lb test ,and will it be likely to hit that the same if you had 6lb? or does it matter?

imo,i think you'd get maybe bigger but less fish , 

what's your opinion?

All else equal, the 6lb diameter should be harder for the fish to see

I know the minnow is a movin but I still like finesse lines where I can get away with them or fluoro

So the rule of thumb is alway go as low diameter as you can get away with.. esp w/ the slower presentation

I think with 6 lb test though you are riding the razors edge if you decide to tussle with a big fish..

You can use #6 as long as your drag is set properly and you play the fish right. People catch 6lb trout on #4 line. Guys have caught big catfish on light line. 6lb fluoro is very common on spinning reels and plenty of big fish have been caught on those setups.

If you are talking crankbaits, the lures will run deeper with the thinner line.

Lighter line also can increase action on some baits... Years ago reading a line study hypo, indications were anything over about 10 pd. line would create noise, as well as additional drag... But I don't see drag being a issue, generally in freshwater, but primarily saltwater... I have always used light line 10 and under for most tactics and 20 for close combat apps.. Though there are exceptions of course....

From a technical standpoint there is a difference in line diameters, casting distance, lure depth and so on.  From a reality standpoint the first fish to the lure is the one I'm catching, could be 1 or 10#, I don't have control over that.