I'm not sure there is really a benefit of EnF over drip if you're using a recirculating system, though I'm sure others will chime in that one is better. I've only used drips on a limited basis. It was more like a hose on a timer.
EnF should be fine as far as those plants are concerned. I was having a lot of success with it growing soy and some strawberries. For tomatoes and peppers I like either DWC or NFT. But to each his own.
A one gallon bucket empty would probably be packed full to the brim with the root system of a full grown tomato plant, so it's probably not big enough to grow them in. Of course, if there are holes in the bucket and you plan on letting the roots grow out of it (similar to a net pot) then it'll be abundantly large enough. This is an issue of your setup.
Peppers, I would think, would grow just fine in that size container.
Hydro may shorten the time to harvest if the plants bloom cycle is dependent on plant size. It will certainly give you larger plants and, likely, give you more and/or larger fruit.

Hey grizzman,

So why would you choose NFT? I would think that since the root mass is large, there would be clogging of the pvc. (If thats what you would make it out of). Is the NFT system more compact? How big of a pipe would you use?

LOL sorry I am really curious.

I wouldn't use NFT for tomatoes for that very reason. I've used it for sweet peppers and a couple of eggplants.
I like it because it's light weight and thus portable. also, when it's time for nutrient changes, there's nothing left in the pipes to affect the new batch. It's also very compact. you can put the pipes as close as the plants will allow.
For the peppers and eggplant I used 2"x 3" vinyl downspout with holes in the 3" face. the drop was 1.1/2" over 4 feet. (I basically put a 2x4 under one end) It didn't start that steep but increased as the plants grew so gravity could over come the root mass.
For Tomatoes, I always use DWC. but I only grow 2-6 plants. If I were growing on a larger scale, I might consider a drip system as it allows you to spread your nutrients out over a larger area more easily.