my normal advice would be go up at least 2 berths, so at least 7 in your case, so from that perspective either tent will do.
next question is how many physical bedrooms you want & how many will be sharing each one - some 2 berth bedrooms can be a bit snug for 2 people, ie just about enough room to sleep if you don't mind being "cosy" (which hopefully you & DH won't but kids sharing might ), but nowhere to put clothes etc.
"big" only seems to count in terms of getting pitches once you get over about 7mx5m (eg camping club sites), so in that sense not much to chose between them, but there will always be some campsites that struggle with anything bigger than a 4 berth tent
In terms of physically pitching the tents they are very similar, so if you can do one you can do the other, so again not much to chose between them.
The thing to think about is how you will use the tent, for example what you will do on a rainy day? - go out anyway or stay in the tent? If it's stay in then more space is good. If you are the "go out anyway" type of family then it's not so much of an issue.
2000HH is "ok", but 3000HH is better obviously.(I personally would go with at least a 3000HH, but then I'm a boy scout ("be prepared" type of person )
In terms of what we have for me DH & 2 kids? - a tent similar in design to the 8 berth one - DH & I can have a huge bedroom & a double bedroom each for the kids + a big living area, but then we like our space
I hope that helps?