Annoying when the manuals are different!
Looks like the (MPPT Range starting from) 120V version was for an earlier model, dated July 09, and the 50V version is more current. Having said that I have known for there to be mistakes in spec sheets before now too. So it appears there were two versions of this model inverter.
All the indications are that the older version really was designed to go with higher voltage 5" celled panels - these were around 180-200w in size, with an average operating current of about 5A. Back at this time there weren't really any 250w panels (like your Solarworlds) - these use bigger 6" cells and have higher current, generally 8-9A, and lower voltages, perhaps 30v compared to 36-37V from an average 200w panel. This is confirmed on the older manual where it shows a max DC current of 6A, while the newer model is 10A.
Your inverter should be reporting the string current that it sees before it does anything with the power - if everything else is the same on both strings (dirt/shade/direction/tilt, etc) you should _overall_ be seeing very similar current from both strings - but they will still very often be different at times too!
If you have the older model, your inverter may well be losing some power as it may be clipping the panels' current a little - a good inverter's MPPT can try and juggle the voltage and current to some extent to minimise the effect on output, but not all can do this, and in any case, the 8+A at STC for Imp (operating current) that your panels are capable of may be a little high for that anyway, for this inverter. Never mind the fact that the old inverter's MPPT range starts at 120v and sometimes the four panel string's voltage will be bumping around at or below that level.
Panel current is related to insolation - how much sun is getting through to the panel - voltage stays comparatively stable throughout the day, but current can fluctuate much more dramatically with the light hitting the panels, even when you may not notice the difference visually much, if at all. Your four panels have been making close to 120V, which indicates that they are all functioning. Remember each panel you add adds voltage to the string, not current. You've _apparently_ been getting a bit less current on the 4 panel string and overall, it should have the same current as the other string if both have identical directions and tilt - the number of panels in a string doesn't affect the current. It may be you have something wrong with a few cells (I'd think this unlikely, but it is possible), or a panel may be in very slight partial shade (even along the edge of one panel, etc), or perhaps the 4 panel string simply needs a bit of a clean!
Different strings will have different current, even with the same panels - of course they should be closer than you have been seeing - but 20% difference on a momentary basis is not unheard of. You are apparently not getting this difference consistently - one of your figures showed that at one point the 4 panel string was making 50% more current than the bigger string, so you can see that current on separate strings really can bounce around a lot. I'd want to be looking at both strings current in the middle of the day on a clear day over several intervals, probably on a couple of different days, checking that both strings actually do have the same direction and tilt, are genuinely unshaded and clean.
Even so, I would still expect losses from the 1kW inverter given the 4 panel string is bumping along at the bottom of its MPPT range, and that the 4 panel string's nominal current is a little higher than the inverter was apparently designed for. But I'd suspect that the low string voltage of about 120v is in any case going to cause substantial losses as the inverter tries to convert it to higher voltage usable AC power.
Unfortunately, you have a couple of variables here that are going to make it hard to diagnose what is causing the lower generation from the 4 panel string. Yes, it's making less power than you expect, but whether that is due to a loss of current from the panels (I'm not entirely convinced) or a loss due to voltage derating (which I'd suspect has at least some part here), it's going to be hard to apportion these losses without measuring each of the 4 panels individually. Even if you did find something, I'd still expect voltage derating losses, so it's highly unlikely that any testing would be cost-effective.
You're pretty much stuck with what you have - getting a new inverter more suited to your panels current and with perhaps less voltage derating too, _might_ help a little - but given the cost vs generation gain, that too is unlikely to be cost-effective.
