What is your ultimate use going to be for the bike? Track use only, street/track mix, canyons, commuter? That may help give a little more input.
1) Is the 2019 R3 that much better than the previous generation? And would it make that much difference to me as a novice? I know the front forks are stiffer, and the rear is stiffer too, with more damping adjustment. If it is that much better, perhaps it is worth the extra $1400, if it means not adding a fork cartridge, changing brakes and tires. I am 6 foot, 200lbs, if that helps.
The 2019 suspension is better than previous years being stiffer, but for a little over $1,400, you could get an older model and put fully adjustable forks and maybe shock that will be even better still. The suspension, body work and ergonomics are the changes for 2019, so frame and engine are the same.
2) I would be looking at swapping out the bias ply tires on the 2018 R3 for track duty. Would I be doing the same with the stock tires on the 2019 anyway?
Being a novice, you'll be fine for a little bit with the Dunlop's. I used a set on my 15 off of a 19 for a track day day and they were much better than the bias plies, but once I started improving, I wasn't digging them very much as they don't have as steep of a profile as more super sport/track tires do. Mine are just sitting in the garage now.
3) Ari Henning and others have said that the stock brakes and suspension work extremely well on the Honda, making it a great handling bike. If so, does this mean I could go with the Honda and forget about upgrades, other than tires?
You'll still need upgrades once you start getting a lot faster, but in your case, you may want them even sooner based on your weight. Japanese manufacturers design great bikes, but the suspension tends to be designed for people on the lighter side. My R3 stock suspension was fine, but I was bottoming out the rear shock in the canyons and I'm 5'10" 200ish lbs with full gear.
Brake upgrades will just be pads really. Pads alone will provide better than stock braking and they're cheap too. (Also, stainless brake lines are a good idea).
Personally, brakes are not as big of a focus until you get fast with small cc bikes because they have pretty aggressive engine braking and when starting out, you won't be likely to be going deep into a corner at full throttle and then immediately to brakes right off the bat. This also depends on the track, but more technical tracks will probably have you focusing more on turn in and throttle control.
4) Does the Ninja handle as well as the R3? I do not need Ninja horsepower. I sat on it and it felt fine, but not noticeably bigger than the R3 or CBR to me, anyway.
I personally feel the main edge the 400 has is more power. R3 edges it in handling and I feel the R3 is a better quality bike, currently. For track riding, another thing to consider is the 400 has clutch/shifting issues that will need to be sorted before you get serious or you'll have finicky shifting and premature clutch wear.
But for an R3 to keep up with a 400 with an equal rider, it will need power upgrades, which fortunately for the R3, there are a lot of out there.
In the end, it depends what you'll be using the bike for most and take weight into account for suspension and speed. Speed may not be a major factor for you now, but as you get better, every bit of power and skill starts to count in areas like corner entry/exit where you can't just turn the throttle and instantly go faster.
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