So I will start by saying that the P-47 is my favorite plane of WWII. So I was really hoping that WG would make it useful but I remained doubtful due to the way 50cal MGs are treated in the game. IRL 32lbs/sec of lead comes from a P-47!
I've played the line up to tier 8 now, which is likely 1 tier higher than I will grind when the patch goes live. In short, the P-47 line plays like the F-4U line but with MGs instead of cannons. I am generalizing. To continue generalizing: Both are fast, medium alt, rolls well but can't turn with fighters, and can carry rockets and/or bombs.
So what's the difference? They are subtle.
1) The P-47s are damn fast. Incredibly fast. Even slightly faster than the F-4U. And the P-47 holds this advantage at all alts.
2) Climbing? Yeah, big time. The P-47N will boost-climb with a 109Z, and will regain speed faster after the climb. The F-4U is a great climber too, but lags behind slightly in this regard.
3) ALL-alt performance. The P-47s have another advantage over the F-4Us here because they retain their performance proportionally better from a higher ideal alt (2000m) all the way down to sea level. This, with the climb rate, makes the P-47s better at hitting GTs (or GAs) and then returning to the fight.
4) Turning. The F-4U actually turns fairly well, the P-47 doesn't. Both roll well, but the P-47 rolls faster and faster as you go up in tier. Overall the P-47s are similar in maneuverability to the 190 line. You can make someone on your tail miss often, but you will never be able to get your guns on him again until you get range to turn back.
5) Guns. Many guns. Many weak guns. High speed + weak guns vs. GTs = bad. The F-4U line is much better at singling out and killing AAA sites. The 20mm on the F-4Us is also better in nearly every way for aerial combat. The one situation where the P-47 line's guns hold an advantage is chewing up large-HP targets that you can camp behind. Contrary to how I play my 50s with my P-51D I actually put sights on my P-47D and N and it significantly increases effective firepower. I attribute this to the P-47's higher closing speed (reduced firing window) and the P-51's ability to turnfight with more types of planes.
I have concluded that the P-47s (and the rest of the line up to tier 8) are best suited to hunting HFs and GAs. Against any MR or LF they need to be used as a HorB&Z, making fast passes at planes already occupied with other targets, then escaping using their speed. Essentially the P-47s are interceptors that happen to be used against GTs too. The F-4Us are true MFs as they can be used against pretty much anything in the sky or on the ground - so long as the pilot knows the pros and cons of the planes involved.
p.s. WG, please increase the range of MGs. Cannons should, of course, hold a distinctive edge. But MGs max range should be increased by at least 50m across all tiers.