Stock-for-stock, your car and his are nowhere near equal. A stock 5.0 GT with a manual
tranny will run anywhere from the high 13s with optional gears, a good driver, and ideal track conditions to mid-15s with 2.73s, a bad driver, or crappy track conditions. Your II on it's best day stock MIGHT break into the 17s.
If you want to be faster than him, you'll need to compare the cars heads-up, see where the differences are:
1. Airflow into the engine; He's got a throttle-body that's overal diameter is much bigger than the two barrels on your carburetor combined, his intake manifold is also a lot less restrictive, upgrade to a 4-bbl. carburetor and intake to address this.
2. Compression ratio; Believe it or not, if you look at the Ford Performance Parts and Interchange guide put out by SA Books, there isn't any significant difference between the cylinder heads put out by Ford for the 302 from the mid-70s to the early 90s. There are minor differences, but nothing earth-shattering, the valves, ports, and runners are largely the same. The big difference here is your pistons. The 5.0 HO uses pistons with shallow valve reliefs that are otherwise flat-topped, your 302 from the mid-70s uses a dished piston that cuts your compression ratio down. Upping the compression ratio brings you to three choices: Change your pistons (full teardown required), aftermarket cylinder heads (how big is your budget? There are fantastic iron heads out there from World for less than $1,000 a pair, yeah, and that's cheap for aftermarket heads), or mill the heads you've got (probably your cheapest option, and definitely not a bad one. If you've got a performance-oriented machine shop in town, they can port and polish your stock heads and give them a 3-angle valve job while they have them for a little more bang-for-the-buck.)
3. Exhaust flow; Look at a stock 5.0, that's right, directly out of the Dearborn assembly plant they have tubular-steel shorty headers, pretty spiffy, and not very restrictive. Now take a look at your stock Mustang II, that's right, massive, restrictive, ugly cast-iron exhaust manifolds. Get a set of headers, or have a machine shop port your manifolds (cost is about the same, so unless you're horrified at altering the look of your engine compartment, headers are pretty much the way to go). Look further, and you'll find a restrictive, single, 2" exhaust pipe on your car after the Y-pipe. Looking at the 5.0 reveals a full dual-exhaust system with crossover pipe that is 2 1/4" from the headers to the tail pipes, get an exhaust system done on your car, $200 will have you 2 1/4" pipes and glasspacks from most muffler shops, better-sounding mufflers go up in cost from there.
4. Camshaft; You can't see this one, but the 5.0HO has a massive advantage in this department. Equipped with a roller-tappet camshaft with a relatively aggressive profile (not so much anymore, but definitely when considered against the stock flat-tapped bumpstick in your car). Not only that, but the 5.0HO uses the superior firing order of the 351Windsor. The key to upgrading here is picking the right camshaft for the job. You'll need to be honest with yourself here, because too much lift and duration will hurt you a lot, but too little of them won't absolutely kill you. Don't go buying "camzilla" just for the rough idle, you'll need to match the cam you buy to the other upgrades you do, and you'll need tech help on that from someone like Comp Cams.
This is by no means an exhaustive list of what you could do to make your car competitive with or faster than his, it's just a good starting guide. Other things that would be basic upgrades on a Mustang II would be wheels and tires, gears, traction bars, shocks, and a performance fuel pump to match a larger carburetor.