Which one would yield the bigger benefit for me and my road bike?
No question: pedals. Absolutely no question IMO.
Personally I saw no speed improvements going from toe-clips and straps to clipless pedals. Clipless pedals are nicer and do have benefits, but speed is not one of them.
I’d go with the clip-on aerobars.
You what?!
Pedals - no arguments.
YES - check out eBay or local people for picking up some aerobars used cheap and get the pedals as well!!
Oh, I always have questions, Tom. 
How much of an increase in speed will I likely see from clipless pedals? (I know, I know, it’s individual, blah blah blah. . .But are we talking about 0.1 mph, or 1 mph?) I understand the rationale behind clipless pedals, but I can’t picture them making me faster. Just looking for reassurance.
I think it would have to do with whether you are riding clip pedals with straps with a hard soled shoe or a running shoe and also which distance(s) you are focusing on. If you are riding with running shoes and trying to do longer distances then I would assume that your feet are currently taking quite a bit of punishment that would be relieved with clipless and a good pair of shoes.
I’d go with the pedals. The pedals give you the opportunity to deliver more power more smoothly than without them, whereas the aerobars will allow you to minimize your profile and (hopefully) reduce drag. If your option is to deliver more power more evenly throughout your pedal stroke with less fatigue, or to have less wind resistance while powering your bike for only 80-90 degrees with each leg, which would you rather do?
I consider myself to be pretty inefficient with my clipless pedals, but last week I got on my wife’s bike with platform pedals and I found myself lifting my feet up off the pedal trying to pull them up.
pedals. but don’t forget you have to buy shoes then too.
To be honest you’ll want both. I knocked nine minutes off a 30 kms on my old 12 sp by using both. For aero bars get shorty ones designed for a road bike geometry or a size smaller (Syntace C2’s for example) tri bar than you’d use on a tri bike, other wise you’ll be too stretched out.
To be honest, what I want is a Dual. 
I’d like to be able to get both, CG, but I don’t see it happening. Mainly because, as someone else pointed out, I’m gonna need shoes to go with the pedals, and shoes look like they cost 'bout 100 bucks, minimum.
Think I’ll be going with the pedals for now. At the very least, they’ll look cooler than my toe clips and white running shoes, and that counts, right? If I find out the slam position will work for me and my long legs, maybe I’ll just add the C2s to my bike later, and forget about a true tri bike altogether.
As someone else pointed out, you can get pedals, shoes, and clip ons very reasonably on eBay.
One other advantage to pedals is that you get to use different muscles. You can pull on the upstroke as well as push on the downstroke. Having a good set of pedals translates into much more efficiency.
If you can make the slam work it’ll save you money. It works great for my wife but not for me. The bars you’ll probably want are the Profile Jammer GT’s or the Oval version for the slam.
I’m sure there are some good deals on eBay, but I really would prefer to buy locally.
Besides, no way am I going to buy my first pair of cycling shoes on the Internet without trying them on- what gives with the metric sizing? I thought this was America, sheesh!
Cycling is a non-US sport, and the rest of the world runs on metric. Let’s face it, if Lance isn’t in it, no one pays attention here in the US (even with Lance the TV viewership is somewhere just ahead of the Pro Bowling Tour…) Compare that to the vast throngs of spectators - yes, actually AT THE COURSE AND NOT JUST IN THEIR COUCH WATCHING - that will come out to a major TDF or Giro stage.
Two things about eBay - First, try em out locally, and buy online. Second, don’t EVER buy from someone who won’t let you return em. This goes for both new and used items. Any quality seller will allow returns, PERIOD. If they don’t, AVOID THEM.
im not Tom, but with clipless, you get an effecient pedal stroke, esp w/ hard soles. Thus, youre less tired for the run. I would say overall, for an oly, 25 min off your time (unless youre already really low, so from 3hrs to 2:30), exponentially more for longer distances. I would also say clipless would lead to less injuries.
If your option is to deliver more power more evenly throughout your pedal stroke with less fatigue, or to have less wind resistance while powering your bike for only 80-90 degrees with each leg, which would you rather do?
Actually, I think that’s an excellent question. I don’t know.
First, how much less wind resistance would I get from a set of shorty aero bars?
I thought with a name like vitus 979, you would have a pair of wooden-soled, Detto Pietro shoes with nailed-in cleats and Campy Record (or at least Miche) quill-and-strap pedals. What is the worl coming to these days?!?
Pedals and shoes FIRST. Performance has some real, live LOOK-produced pedals for under a c-note. Shoes- you don’t want to skimp- get a close-out pair of Carnacs, Nike, or Sidi (whatever fits best). You could get away with spending not bunches of money.
Why do I say clipless? The stiffer sole of a proper cycling shoe, along with the integration of foot and pedal (via cleat) will make you more efficient, thusly making you a faster and more comfortable cyclist.
I could play Devil’s Advocate here, however: Pyro platforms, a pair of clipless pedals (can be pretty cheap, AND a pair of shortie clip-ons could be done for under $300, cheaper if you look for sale/closeout/blowout items. Am I a huge fan of Pyros? Only if you do sprint distance duathlons where transition time is key.
Pedals without a doubt
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This reminds me of a race I did two years ago. Saw a guy riding barefoot on metal “claw” type pedals. Lter saw him running barefoot, he was pretty fast. After wards, I asked him about it, he said he was in the Air Force, wore boots all the time on duty, so he went barefoot whenever he had the opportunity. Maybe the clip-on bars would help more?