My advise would be to, first, check this out here http://www.youtube.com/watch?gl=CA&hl=en&v=Mze7-zhkx-4 and follow his tips on how to live in up a Marshall 1960A cab. You may find it makes THE difference your looking for.
If it doesn't and you are still looking for a new cab, I would personally suggest a Mesa/Boogie "4x12 Stiletto Traditional Straight" as shown here: http://www.mesaboogie.com/Product_Info/Guitar%20Cabinets/StilettoCabs/Stiletto4x12TRst-LG.htm
I have an over sized recto cab (slant) and it sounds great, but from the reviews and research I've done online and from what my ears tell me I believe the recto's may be more suited to Nu Metal type tone, where as I look for a tone more like Hetfield's Justice tone...He used a Marshall straight 4X12 with V30's I figure this is as close but more than likely better quality as it's a Mesa! And based on the description on Mesa's site this cab sounds to be what your lookin for:
"STILETTO® TRADITIONAL cabinets are slightly smaller than our Rectifier® cabinets and produce a tighter, more balanced low end response with an emphasis on attack. The midrange is more pronounced and this cabinet is often preferred for styles that require a tight tracking, articulate response."
When they list this cab as being smaller, I beleive it's smaller in comparison to an over sized recto cab which makes it smaller yes but the same size as a traditional 4 X 12 like your 1960A so it's not really "smaller"...
Let us know what you decide post results.