If it's cheaper to get the 1020 from Waterloo, I'd get that, rather than the 1006 from Paddington.
FGW trains may look like 'InterCity' trains but inside they're designed purely for commuters, with very few tables. and hard seats. Do they even have 2 tables opposite each other any more? I'm not sure. By contrast, SWT trains may look like commuter trains but inside they're actually more like InterCity trains, and are more comfortable. It should be possible to reserve all 7 of you at two tables opposite each other on SWT (are you using 2 x Family Railcards to get discounts for all of you? If so it may be worth booking 1 additional CHFAM ticket, at minimal extra cost, to fully reserve 2 tables for your group).
On the other hand if FGW is cheaper it's probably worth it and at least it's quicker so you don't have to endure their uncomfortable trains for too long.
I am surprised First Class was recommended by TheWalrus because you would not get a discount in First with a Family Railcard. I'm also not convinced that FGW offer free beer either in First? Free tea, coffee and soft drinks, yes. Are FGW staff better than SWT staff? I'm not sure, both have a reputation for having some unsympathetic staff with a poor attitude toward customers, but the majority of staff will probably be fine on either operator. Also I am not convinced with TheWalrus that FGW HSTs have more legroom than SWT 159s. It's not my area and I've not measured the legroom, so maybe he's right, but it's not my recollection.
FGW trains may look like 'InterCity' trains but inside they're designed purely for commuters, with very few tables. and hard seats. Do they even have 2 tables opposite each other any more? I'm not sure. By contrast, SWT trains may look like commuter trains but inside they're actually more like InterCity trains, and are more comfortable. It should be possible to reserve all 7 of you at two tables opposite each other on SWT (are you using 2 x Family Railcards to get discounts for all of you? If so it may be worth booking 1 additional CHFAM ticket, at minimal extra cost, to fully reserve 2 tables for your group).
On the other hand if FGW is cheaper it's probably worth it and at least it's quicker so you don't have to endure their uncomfortable trains for too long.
I am surprised First Class was recommended by TheWalrus because you would not get a discount in First with a Family Railcard. I'm also not convinced that FGW offer free beer either in First? Free tea, coffee and soft drinks, yes. Are FGW staff better than SWT staff? I'm not sure, both have a reputation for having some unsympathetic staff with a poor attitude toward customers, but the majority of staff will probably be fine on either operator. Also I am not convinced with TheWalrus that FGW HSTs have more legroom than SWT 159s. It's not my area and I've not measured the legroom, so maybe he's right, but it's not my recollection.
This confusion is something TOCs and companies like TheT***nLine have caused with their vagueness about "buying online for cheap tickets".