How much bike upgrade with new bike?

All other things being equal...

You can expect the new bike to be a pound or two lighter.  Friction is a function of force, but the coefficient is pretty low, so figure <1% improvement in rolling resistance (tires and drivetrain) due to lighter weight.  

You can expect some improvement in bearings, so your coefficient of friction might go from 0.01 to 0.005.  See above.  

A 30-year-old Cannondale probably has a 6-speed or 7-speed rear derailleur, possibly 8-speed.  Modern drivetrains in your price range will be 10-speed (I think).  You can remain in your sweet spot over a wider range of conditions which will probably be the bigger impact (maybe 3-5%) improvement.  

With the reduced weight, you'll notice more responsive acceleration to increasing effort so you'll feel like you're making bigger gains than you actually are.  This will make a difference if you ride rolling courses.  

If you like riding your Cannondale, keep riding it and spend the $1000 in other ways.  Coaching, aero helmet, aero wheels, vacation, more races, movie night with the family, iPhone 8...

If you don't like riding the Cannondale, buy something else (at the expense of some of the above alternatives), but know that you it'll be hard to determine whether the improvement is because of the bike physics, your enthusiasm with the new toy, or better fit.  

I have been rocking a 1988 Peugeot for several years and have invested about a grand into it. I have gone from the original 6sp to a 8sp setup. Still clicking downtube shifters. Upgraded the derailers and brakes to Shimano 600's. (Ultegra grade back in the day) Ditched the quill stem and went with a modern stem setup so I can use different setups to position the handlebars to my liking. I also went to modern ergo handlebars. My biggest 'fit' improvement was a custom 155mm Sram Apex crank setup with modern BB. This allows a more aggressive position on the bike. Next upgrade will be a set of modern wheels, right now I am running a staggered setup with 25mm in the rear and 22mm up front. (I was previously doing lots of aggressive downhill mountain twisties and the wider rear gave me more meat on the ground on those hard leaning high speed turns, fun!)

All of these improvements worked to get me into better position which in turn allowed me to turn more power for longer periods of time. I don't have any hard numbers but I can tell you that with each modification I felt better and made some significant improvements over previous rides on the same routes.

If you like your bike, I would say upgrade it. If your in the market for a new bike, I would set your budget to a more realistic $1,800-$2,300. From my window shopping anything less just gets you subpar components, I would consider group 105 as minimum entry level for a competitive bike. 

Hope this helps.

I actually strongly suspect you'll get quite a significant boost from upgrading to a good racing TT bike!

Note that it wouldn't necessarily be because the TT bike would be so much better of a speedster ride compared to your 30 year old road bike (it's only a small gain in speed at best) but you'd likely have both a better fit (hopefully) which adds the most gain for speed (the bike aerodynamics are puny compared to your body's effect on the wind) and more importantly, you'll likely LOVE riding your new sexy bike which lead you to a lot more bike training and commitment, which will then take you to the next level. 

I'm the last person to advocate getting pricey trigear for looks and bling (I actually run mostly in $20 water shoes now since they're cheap, surprisingly durable, super lightweight and portable, and work well with my minimalist shoe stride) but the bike is definitely an area where having a bike you're excited to ride and look at makes a big difference for the AGer.  

I'll also warn that you probably won't find the ideal tribike for yourself at <$1000 - the options at that range are few and far in between unless you get lucky finding a great used deal. At $2k, and for sure, $2-3k though, you're look at stuff like Cervelo P2 and similar true aerobikes which look and ride awesome, no matter what vintage. There are a bunch of used Cervelo P2s being sold online in various places for well <$2k, many barely used and which look near-mint.