First I will compare the books themselves:
Front Covers:

(Left: Tankoubon | Right: VizBig)
The tankoboun's front cover uses the front cover of the Japanese re-issued release of the Japanese tankoubon. The VizBig's cover might have come from Daizenshuu 1, as Herms said, but I'm not so sure. The logos are different, as all VizBigs use different logos than the actual logo of the manga, and both, obviously, have a big number 1 in the corner.
Spines:

(Left: Tankoubon | Right: VizBig)
The tankoubon's spine contains the Shounen Jump, Dragon Ball Z, and Viz Media logos. It shows an unfinished picture that can only be seen completely if all 42 tankoubon are brought together. In between the picture and the logo says "Akira Toriyama", the author's name, and a 1, indicating that this is the first in a series.
The VizBig's spine contains the VizBig, Dragon Ball Z, Shounen Jump, and Viz Media logos. Under the DBZ logo says "Akira Toriyama", the author's name. Under that, Goku is standing confidently as he is about to undergo battle with the mighty Saiya-jin warriors. Under him is a square box with a 1, indicating that this is the first in a series. Under that shows a rectangular box that says "Three-in-one", showing us that there are three books in one package.
Back Covers:

(Left: Tankoubon | Right: VizBig)
The back of the tankoubon shows Super Sa.... wait a second... What the hell is Super Saiya-jin Goku doing on the back cover of the first volume!? The idea of Super Saiya-jin hasn't even been conceived at the time! Oh, Viz, you and your... fails.
The back of the VizBig depicts Raditz, but he is insignificant, so we will not go any further than that.
Title Pages:


(Top: Comparison of the tankoubon title page (left) and the title page of the entire VizBig (right) | Bottom: VizBig's title page of vol. 1)
The tankoubon's title page depicts Raditz, who dies in the same volume.
The VizBig's title page is plain and black with Dragon Balls towards the bottom and the DBZ logo at the top. Bellow it are the titles of the three single volumes it contains. On the very bottom says "Story and Art by Akira Toriyama". The VizBig's vol. 1 title page is exactly the same as the tankoubon's, witht the exception of the different logo.
Cast of Characters:


(Top: VizBig | Bottom: Tankoubon)
The VizBig pages obviously show much more characters than the tankoubon's, since there are 2 more tankoubon included in the VizBig. Also, there aren't a lot of characters in vol. 1 anyway.
Chapter One - Dialogue/Punctuation Changes


(Top: VizBig | Bottom: Tankoubon)
The VizBig contains a missing apostrophe in the "Wha(')?!"


(Top: VizBig | Bottom: Tankoubon)
The VizBig replaces the tankoubon's "..." at the end of Raditz's sentence with a more appropriate punctuation mark, the question mark.

(Left: VizBig | Right: Tankoubon)
What a big mess the tankoubon's words are in the speech bubble. Luckily, the VizBig fixed it all up and made the bubble neat and tidy!
Chapter Two - Color, Dialogue/Punctuation Changes, Title Page

(Left: Tankoubon | Right: VizBig)
As you can clearly see, color is added to the first page of chapter two in the VizBig, but what's this!? The title page is gone!! Instead, we have a horrendous panel showing Raditz.


(Top: VizBig | Bottom: Tankoubon)
Since the color is missing, the page in the tankoubon looks like porcupine shit. It looks pretty on the VizBig, though.


The tankoubon has a space between y' and never, and the VizBig simply forms one word with it, y'never. Smart.


(Top: Tankoubon | Bottom: VizBig)
I literally ROFL'd when I saw the tankoubon's horrible butchering of what is supposed to be "Suushinchuu". REALLY!? Soshinkyuu? Is that even a word? Thank Kami-sama the VizBig fixed it.

(Left: Tankoubon | Right: VizBig)
Confusion? What's up with the black/white action bubble?


(Top: Tankoubon | Bottom: VizBig)
No color on the tankoubon. In the tankoubon, Raditz talks like a super hick (growed).

(Left: Tankoubon | Right: VizBig)
The sound effect word things are designed differently, the VizBig having solid color in them and the tankoubon are shaded. Also, the same white/black bubble thing is visible when Goku yells out "Kuriri..."
Chapter 3 - Title Page, Dialogue/Punctuation Changes

(Left: Tankoubon | Right: VizBig)
In the VizBig, the previous page is colorful, but... gasp! Yet again, the title page is missing! But at least we get a cute little panel of Gohan!


(Top: Tankoubon | Bottom: VizBig)
"Usta" VS "Used to".... Hicks.


(Top: VizBig | Bottom: Tankoubon)
Rearrangement of words? The first time looking over these two, I was like... Wha'?


(Top: VizBig | Bottom: Tankoubon)
Hmm... Goku must have hit his head hard.... (tankoubon)


(Top: VizBig | Bottom: Tankoubon)
Yeah, I noticed... the dialogue change. *Insert crickets here.*
Chapter Four - Counting, Dialogue Changes


(Top: VizBig | Bottom: Tankoubon)
Good job, Raditz, now we know you're not a total dipshit who can't count.


(Top: VizBug | Bottom: Tankoubon)
Bulma's line is a total switcherooni! Wait... "Don't mention it!" doesn't even make sense in that context!


(Top: VizBig | Bottom: Tankoubon)
Way to be specific, Goku (tankoubon).


(Top: Tankoubon | Bottom: VizBig)
(tankoubon) GREAT SAIYAMAN SPOILER!
Chapter 6 - Censorship (Swearing)


(Top: Tankoubon | Bottom: VizBig)
(VizBig) I thought Goku was a monkey, not a dog!


(Top: tankoubon | Bottom: VizBig)
That's just plain weird... "Agh"? Really? It seems so overused.
Chapter 7 - Censorship (Swearing)


(Top: VizBig | Bottom: Tankoubon)
Yeah, Piccolo, you better be sure it's going to work - or I'm gonna curse again!
Chapter 9 - Name Switcheroonie, Censorship (Swearing)


(Top: VizBig | Bottom: tankoubon)
By the way, Viz, you spelled "sayounara" wrong.


(Top: VizBig | Bottom: Tankoubon)
Ooooh, I'm telling!
Chapter 10 - Censorship (Swearing), Stupid Grammar Errors


(Top: VizBig | Bottom: Tankoubon)
Somehow "Curse you" seems cheesy; "Damn you" seems much more badass.


(Top: Tankoubon | Bottom: VizBig)
"Ass". Best. Piccolo. Line. Evar.


(Top: VizBig | Bottom: Tankoubon)
(Tankoubon) LEARN ENGLISH GRAMMAR. Oh, It's fixed. Good job.
And that pretty much ends this comparison. Which one is better? That's for you to decide.