Just for clarity Strat> a/b box > a. cable to one amp >b.cable to a second seperate amp?

You have the cable from the guitar going into the INPUT of the A/B and the cables to the amps going from the OUTPUTS?

If yes to above, most likely bad cord between the guitar and box or defective switching or connections in the box. Try each cord seperately from guitar to amp
Then add box between guitar and one amp etc. Because this is exactly what these boxes are designed to do. I use one frequently on stage no problems.

Yes, that's how I have it hooked up. Anyway, I've been trying different things over the course of the night. For some reason no matter what I do, the two Line 6 amps just don't like each other. I tried hooking up the big Line 6 in the same fashion with a Cube 30 in place of the smaller Line 6 and it worked fine, save for some noise going through the Cube 30. The Line 6's end was totally clean.

I'd still like to find a way to hook up the switch box to the two Line 6s but I have a feeling it just can't be done.

I use a Morley A/B pedal to do the same type of thing (two Fender amps) but you should be able to do this with two Line 6 amps. When I first tried to answer your post I glanced at the Apex units specs and thought they were pretty similar but upon deeper inspection I noticed that the schmetatics are different. The Morley pedal has two 100k resistors in the switching circuit. I included links to the schmetatics below.

Electronics is not my forte, I am a gozinta/gozouta kind of guy. Maybe someone with more elec. background could answer this as I am very curious now.

Apex ASB
http://www.apexelectronics.com/downloads/manuals/omasb1.pdf

Morley A/B
http://www.morleypedals.com/abyes.pdf

Sounds like a ground loop problem. Is this actually a buzz or more of a hum? Do you have a cable that could be converted to a ground lift cable? That is, take a cable and remove the connection to ground at one end. Use that cable to connect one of the amps to the AB box.

Definitely a buzz. It got louder or quieter depending on how high I had the distortion set for. However, I was trying to record a distorted guitar so the more crunchy I tried to get it, the bigger the buzz came out.

Originally before trying the switch box, I was just using a Y cable and was having issues even getting signal through both Line 6s but I think that may have been a phase issue. I'd tried the same thing with my two Cube 30s and got the same noise (which may be a ground loop as you said) that I got through the one Cube 30 using the switch box when I tried to split between the large Line 6 and the Cube 30.

Did you try Bob's suggestion?

Also are both amps plugged into the same outlet? If they are it should reduce the potential for ground loop.

I'm not all that electronics savvy so I don't know if I really want to tamper with the cables I have (at least until I start working again and can afford new ones). That said, no they weren't plugged into the same outlet. Maybe I should try that. They were in different rooms when I tried it originally.

Try using a pair of passive (transformer) DI boxes back-to-back between the amps. You will need to interconnect the XLR sockets using a gender-changing cable. This configuration will isolate the amplifier grounds from one another and should solve the problem.

This certainly does seem to be a ground loop issue. This simply means that the gear that's tied together (in this case, the 2 amps) are "seeing" 2 different ground paths. The cheap and easy way to alleviate this is to plug BOTH amps into the same outlet. If you need to use an extension cord, do so, just be sure to use a decent one with a 3-prong grounded plug on it.

Bos's suggestion is the professionally correct way to deal with this issue, especially if you're playing onstage in a live venue and are tied to a sound system. What you NEVER want to do (and there are many dingalings that will tell you it's OK to do this!) is to use one of those 1$-store ground adapters that changes the AC power cord plug from 3 to 2 prongs. DON'T DO THIS!!!! It is very dangerous.