My answer is long so prepare yourself.....
I have a TVS. Friends have Honda, Hero Honda, Bajaj and recently, Yamaha has joined.
You made a good decision by coming down to TVS and Yamaha because Honda doesn't have a performance model now & Bajaj and Hero Honda is what we (me & my friends) hate because only TVS is still in the pink of its health after throwing so much punishment at the bikes.
If I were you, I'd purchase the R15, and here's why:
It has the highest power-to-weight ratio for any 150cc bike in India. Has got 4 valves...see more valves help in better engine breathing which in turn aids in more power with greater response. Its like breathing as fast as you can with your nose jammed when you catch cold (comparable to 2 valves per cylinder) vs. breathing as fast as you can when you are in the pink of your health (like 4 valves per cylinder). Some engines are designed in a way that the second intake & exhaust valve comes into action upon crossing a particular rpm speed. I hope you now understand why more valves are better if performance is a requirement...but mileage suffers in such cases.
When Bajaj said that Pulsar 200 and Avenger 200 are liquid cooled, it was a trick. Bajaj misled people by never actually telling what it means by liquid cooling. These bajaj bikes still had fins on the engine cylinder for heat dissipation...Their engine oil was cooled with a kind of radiator. Yamaha R15 is the first bike in India (if you ignore superbikes) to have liquid cooling. The engine cylinder has a jacket covering, surrounding it which circulates the coolant cooling the engine. Liquid cooling is far better than air cooling and is a boon for racing and long drives (or for that matter, rash driving). Look at any R15 engine cylinder (inside the fairing obviously) and you'll see no fins. Solid metal...its because of liquid cooling. The stylish fairing has the radiator (yes, R15 has got a radiator) for cooling the engine coolant.
R15 has mono shocks...these are always better for high speed handling, stability & improved cornering ability.
For the fuel injection, R15 has 4 sensors spread around the ECU and the engine. Now that's technology
R15's chassis is also different...deltabox frame. If you don't know this, it might surprise you but half of the bikes soul lies in its chassis. The entire ride characteristic of the bike primarily depends on a chassis. The bikes handling, cornering ability, agility...they all are first because of the chassis and then because of the suspension etc. etc.
The features mentioned above are for direct comparison with the RTR180. R15 is still overpriced by a few thousands but it almost deserves its price tag because of the above mentioned things.
Also, when compared directly, R15 has 6 gears while RTR180 has 5. Both have same power but R15 is technologically more advanced as you read above. Tyres of R15 were specially developed by MRF with inputs from the R15 design team so don't worry that they are "puny" and wont provide grip...they are awesome.
Brakes wise, as you have driven both, I think you'll agree that RTR180 has better brakes. Acceleration too is more in RTR180, less in R15. Both will return you the same mileage. R15 looks much better...I just hope Yamaha would launch it in white like the 2009 R1. R15 has better headlights, better handling, stability. R15 also weighs much less...that means you can attack corners with much more ease & confidence.
Don't worry about handling in traffic...see the bike has longer wheelbase which means it will be slightly difficult to control at 5 Kmph when compared to Hero Honda Splendor but long wheelbase is to improve high speed handling. Its a trade....but you'll find it easy once you are set on the bike. Its not bad enough to scare you away!!!
The bike is slightly wide compared to the RTR180 which is naked. That means a greater risk of scratch/dent from some crazy person around you and yeah, it'll be difficult to take out of tight situations (a cycle is the best to navigate through traffic ha ha haa). But don't worry at all...
Look cost of ownership for R15 is high because of things like 4 valves, full front fairing, liquid cooling, radiator, various connecting hoses etc. etc. R15 spares are costly. If that is not a problem with you, go for R15 with your eyes closed and don't worry about the commuting in traffic thing. Of course it'll be easier in the RTR180 but I don't think it is a reason good enough to stop yourself from getting the R15.
But consider this:
How many people to own a R15 or a Pulsar 220 or RTR180 drive the bike above 120 Kmph every single day? In a country like ours, traffic and the roads are a nasty nightmare for we bikers. I race with people very very rarely on a highway. Most of the times its in traffic...cutting through.
What I'm saying is that RTR180 has, when compared to R15, better acceleration. Meaning RTR180 will cross 80 Kmph faster than the R15. R15 will win on the highway but in city, RTR180 will. RTR180 has better brakes too. And if you crash on a R15, it means you get a big hole in your wallet for costly spares. TVS spares are costly when compared to Hero Honda or Bajaj but cheaper than Yamaha. Apache RTR180 costs much less too. Then both have same power, same mileage.
Think this again that how many people having the R15 cross 120 Kmph everyday? Will you? If your answer is no, I don't think spending another 35,000 for a bike with 6 gears, liquid cooling & mono shocks is wise, justifiable.
The Apache RTR180 is a very good bike & having a bike without 4 valves, liquid cooling, fuel injection, mono shocks isn't a bad thing either. Remember that the racing division of TVS i.e. TVS Racing has won almost all national level events (Yamaha too has won...Hero Honda & Bajaj don't even have a racing division) and some respectable Asian level racing events too and much of TVS's racing knowledge has been used in its commercial bikes since the days of Fiero.
Go for RTR180 if you aren't going to drive above 120 Kmph quite often. RTR180 will be a better option for traffic and I assure you, TVS is all quality & can take whatever you throw at it. RTR180 comes second only to the R15. RTR180 has great chassis, suspensions, brakes, stability and is very very nimble, agile.
I promise you'll be able to handle both R15 & RTR180 with ease. That's one of the quality both bikes have!!!
There are people who'll say that the seating posture on the R15 or the RTR180 will result in back pain. Simply ignore them...they haven't taken the bikes for a long drive. You'll get back pain only and only if you've a weak back, shoulders. A normal person will never have a problem on them (at least I have still not got back pain).
I have a feeling that my answer will puzzle you a bit more, but all the best!
Menace was RTR180's code name when it was a secret project & TVS was working on the bike. Now its no longer Menace. Its simply TVS Apache RTR180.