The RD125DX was not a commuter bike. It was an all out sports bike. (using the technology of the day). It revved to about 10,000 rpm and had a top speed of almost 80mph.
It had 16bhp and was later restricted (after 1981) to 12bhp. It was a reed valve 125cc 2 cylinder air cooled 2 stroke. It was slower and less powerful than an unrestricted RD125LC because it was air cooled rather than liquid and it did not have an exhaust power valve.
However, you have to have passed your motorcycle test by 1981 to be allowed to ride a 125cc bike with more than 12bhp, unless it was registered before August 1st 1981. This meant that you could legally ride either a full power (16bhp) RD125DX, if it was first registered before Aug 1st 1981, or you could ride a 12bhp RD125LC if it was registered after that date (all of the RD125LC's were made and registered after that date).
So the fact that the RD125LC could produce almost twice as much power as the DX was irrelevent. The market it (RD125LC) was aimed at in the UK was the learner rider with a provisional license who was restricted to 12bhp. If you derestricted it to unleash it's full potential, you had to technically pass your motorcycle test first. This means that technically speaking you are better off, in terms of power and performance, with the RD125DX (if registered before 1/8/81) than with a legal RD125LC.
Of course if you break the law and use a derestricted RD125LC, before you have passed your test, then you are better off with an RD125LC. I have never heard of anyone ever being charged with riding a derestricted 125, but anything is possible. They could stick it on a dyno and test the power. The only reason they would have to do that though is if you were stopped doing 100mph; there's no way to squeeze that out of 12bhp. I guess even then it's highly unlikely they would test the power output; you'd be in enough trouble anyway.
The RD125LC (all three incantations) were 12bhp water cooled 2 stroke single. They were restricted to get them down to 12bhp; the full power unrestricted models were almost 30 horsepower and good for mid 80's to low 90's. With a small amount of tuning they can do the ton. With a small amount of tuning, i.e. exhaust and KN air filter, they will produce between 30 and 32bhp.
Me and my brother used to hack about on a 1984 RD125LC, we had it up to 27BHP and we were using it on Provisional Licenses. We never had a 100MPH out of, but did get it up to 98MPH downhill on the A1. In the end my brother dropped it at 60MPH, and it carried on sliding on a wet road straight into a crash barrier where it burst into flames. That was the end of it, we had not bothered to register it so we just left it where it fell. Happy Days.
I had a 1986 RD125LC, I bought it second-hand in 1989 for £600.
I think it must have been tuned because it had hardly any power below 7000rpm, then it would enter its narrow powerband and lift the front wheel in first or second gear.
During the 4 or so years that I owned it, I fitted a four-piston caliper from a Suzuki RG250, Allspeed exhaust, Aluminum swingarm and rear wheel with disc brake (from the RG250), flat-slide carb (RG250 again), 190cc big-bore kit and I removed the balancer shaft from the crankcases. There were loads of other mods which I can't remember now, I last saw the bike in 1993.
It would do an indicated 105mph on a good day and was lots of fun, handling was OK for its day I suppose. It taught me what 'tank-slapper' means, then I bought a steering damper.
I owned an RD125LC mk2 in 1986. It was brand new in red and black and cost me £1050. I installed a racing clutch after destroying the original, filed the reed block to the edges of the reeds, and fitted racing reeds, up jetted, removed the air box, fitted a K&N filter and an Allspeed can. Not sure what speed I was actually doing, but regularly saw the end of the clock. I ended up fitting seven pistons in total (kept blowing it up).
It eventually got nicked. I have recently bought a wrecker to restore, and that cost me £800. If only I knew then; such is life!