There are continuity problems between one series and the next. Most of them are rather minor character personality changes, art styles, and music, but there are a few big ones: GENOM was absent in BGC!, the Boomers were stupid, ADAMA didn't seem all that special, and the world itself was lighter. All of those things can be looked past or explained by anyone who really wants to enjoy the series, but most people tend to think that it took place in an 'alternate universe.'
Toshimichi Suzuki stated in an interview that BGC! was essentially what the final episode of BGC would have been, and he himself stated that the series were in fact connected. There are also novels and at least one manga that serve to connect the two. Soldier Blue, written by Suzuki himself, is the link between the two series. However, Soldier Blue was admittedly... odd... and therefore is hard to consider canon, even though it was written by Suzuki.
The end result is that it all depends on how someone wants to view the series. If you're picky then you probably won't think Bubblegum Crash! is worthy of the word "Bubblegum." If not, you'll probably enjoy it.
Why Is BGC's Sequel Called 'Crash' and Not 'Crisis?'
There are a few reasons for this (there are always are). First, according to some sources which argue with others, ADAMA was special because he was entirely synthetic, not at all organic. Without the organic brain that most Boomers had, his head had to be enlarged and his body type changes drastically to house the more advanced computer systems. The reason behind him being inorganic was that supposedly this would cut back on Boomers going mad because their organic systems were damaged. It seems to me personally that if my microwave acts up, ADAMA could too, but that's just me...
Second, ADAMA could 'talk' to the SuperComputer in Geocities. None of the other known Boomers could do this. Apparently Largo could, though; that's where he got the information on ADAMA's AI.
ADAMA was also supposed to be more personable and intelligent than most Boomers. Obviously he was smarter than the average BU-55C. He could also come to conclusions about problems without having to have the situation explained in full the way that the generally stupid combat Boomers would. He had no built-in weaponry but he was all the more powerful because he could crack into nearly any Boomer's mind and alter its programming. This would make ADAMA a very useful tool in electronic warfare, among other things. These are the reasons that Sylia was so hell bent on rescuing him. She knew that others could perverse his mind and abuse him as they did most other Boomers.
Where Is BGC! Music Available?
What Are the Characters' Sexualities?
It has been questioned time and time again if Priss is a lesbian. The answer seems to be No. Her lover from before the Knight Sabers was a male, she had a developing relationship with Leon, and the whole of her band, aside from herself, was made up of males. Priss' relationship with Sylvie was only different from her relationship with Sho in that Sylvie was a buxom female who happened to have many of the same interests that Priss had.
Is Nene a lesbian? The reason people think this is because she is so attached to Sylia that it's scary. It's more respect than anything else, I believe. The other thing that makes people wonder this is that she was utterly obsessed with telling the world how good looking she thought Sylvie was. That's a little more questionable, but still pretty normal by Japanese standards. She also has a potential relationship with Mackie, who is definitely a male.
The only reason anyone has ever questioned Linna is because she was shown once without her headband while Priss was washing dishes in her apartment. That's a really bad reason. She only wears her headband once during all of Double Vision but nobody wonders if she slept with Kou. Thinking Linna's a lesbian is ridiculous.
Finally, there's Sylia. Sylia never does or says much of anything to indicate that she even has a sexuality. She's possibly asexual, which means that she is not attracted to anyone. She displays some heterosexual thoughts when she jokes about the others' boyfriends in various episodes, but aside from that seems totally detatched from the world of sexual cravings.