I'm a bit of a Skyline junky, so take what I say with a grain of salt.
The Skyline series, if Lakland's marketing to to be believed, are "assembled" overseas from US designed parts. The electronics and hardware are the same as the US models. There are some minor differences in the nut and the necks of the US ones are quarter sawn. The US models also have a lot more finish options and can be built to order. The Skylines are massed produced and you have to just go with what is available. I don't know where the Asian models source their wood from.
Some people have made a fuss over whether they were assembled in Korea, Indonesia, or where ever. I don't care too much about that, but I'm picky about the years only because I prefer the Bartolini electronics over the LH-3 electronics.
Tone wise, the US and Skyline models are near impossible to tell apart. When I bought my first one new in 2006 I was flush with cash and could have bought a US model, but after playing both, couldn't find a reason not to buy the Skyline for half the price.
The 44-01 and 55-01 basic design is similar to the staple 44\55-02, but with a simplified electronics package. The -02 is where it is at. It is one of the most flexible designs you will come across. Instead of switching between serial and parallel, the MM humbucker splits, giving you a MM tone, a 70s jazz tone, and a 60s jazz tone. The single coil at the neck does a great imitation of a P bass and its dead quiet. The pan, three band EQ, mids adjustment in the cavity, and spliter give you an endless supply of tones. The biggest downside is the Bart and LH electronics are a little on the polite side, meaning if you like the gritty snarl of open pole piece pickups like Seymour Duncans, you might find the Skylines a little subdued in the highs. The jazz settings will never give you a Fender Marcus Miller or Geddy Lee brightness. The articulation is very high-mids focused.
Because they are Asian assembled, the Skylines don't hold there value at all. They go for $1400 new and $700-800 used; so a roughly 50% loss of value. If you buy one new, you are screwed. If you buy one used, its a tremendous value. I now have three; a maple and natural finish 4, rosewood and black finish 4 with a tort pg, and a rosewood and black finish 5. The 5s are 35" scale BTW, which is a must for me. I also like the string-through-body construction.