I don't think it is SG government's interest for SG to be well-connected to JB via roads. Investors and more Singaporeans will invest and spend in JB instead if JB is so well-connected to SG. So expect more jams ahead :p
The option isn't invest in JB or invest in Singapore. Those are 2 options. Other options are invest somewhere else and move operations completely away from the Singapore area. Or just don't invest in the Singapore area because the costs are too high (or you can't get workers, or the infrastructure in Singapore is too crowded so you can't expand…) - so investments are just not made.
It is the same thing that happens elsewhere - you have a high cost central city and a lower cost suburban area. There are tensions between those two (or more) bodies - as they are often different tax entities and different elected officials. But for the city to prosper they must integrate with the larger metropolitan area (or growth just slows drastically, even crashes potentially - due to limited space, high costs and businesses options to just go elsewhere). Manhattan the surrounding area is a good example of doing it right over the long term (and they still have had plenty of issues). But both Manhattan and the surrounding areas are much better off due to the cross benefits each offers. Hong Kong is likely another area though I am not as familiar with how well it is done.
I am sure the Singapore urban planners know this. The question is if Singapore still has the ability to think long term and plan as wisely as it has in the past or not. I think the struggles recently open the door to doubt about the willingness to think long term versus giving into powerful interests that don't care what happens 5 years from now they just want to maximize their immediate gains. That is what happens in many places and why places like Singapore did so well for so long. Singapore prospered by provide a much better urban environment (this includes many things, like investing in education, creating a good environment for business but also providing protection from bad externalities [credit crisis, environment damage, overburdened infrastructure…]) in addition to smart zoning and investing in mass transit etc.) than those that gave in to short term thinkers.
Singapore still is significantly better than most other area but there are complications that grow as the population grows… It requires better management to manage Singapore to even more prosperity today than it did to keep things going in 1995. I believe Singapore continues to be acting intelligently the question is if they are slipping some and the challenges are growing whether they will suffer - or will they rally and continue what has been a very good progress for several decades (though most acknowledge there are more issues and frustrations the last 5-10 years).
Johor's situation is actually much easier to manage. Really it is more about not doing bad things than doing anything incredibly well. The issue is when you look around the globe for the last 50 years lots of places have not only not done incredibly well but have done really bad things for their economy. The evidence shows most states/governments will mess up more than than avoid messing up. I think Johor has been doing very well the last 10 years but that is not very long and the situation was not very hard - basically avoid doing lots of bad things and you will do well. If they can continue things will go very well. Also success creates problems - fast growth is hard to manage in urban planning unless you really do smart things. Johor is going to have fast growth and has been having some already. If things haven't been planned for well, by the times problems are visible they may well not be manageable in any realistic way (look at the horrible traffic in KL for example).
Transportation is a big risk of creating big problems, in my opinion. So is not creating enough high paying jobs in JB itself. There are some being created which is good. And their are even more decent jobs being created which is good. But there is too much luxury housing and not enough office building in my opinion for a long term stable, strong economy.
The build up of education and medical and tourism has been very good. Medical especially is
great at creating lots of very good jobs (and they will get better over time if things are done right - part of the appeal now is lower costs but over time you can move up the value chain). Tourism (and throw in general retail here) doesn't create so many great jobs but it creates lots of jobs and tourism gives a good source for lots of taxes (taxing people that don't vote is always nice which is why you often have lots of tourist taxes - hotel taxes etc.). Education is decent but really doesn't create a huge number of great jobs.
Banking/finance/insurance would be a good target (especially - back office operations for Singapore, in the next 3-15 years). Technology and internet would be a great area but there is a long way to go - even luxury condos completed this year don't have fiber internet connections that is not the sign of an area committed to 21st century technology. This technology entrepreneurship area is something that needs more support (even Singapore throwing lots and lots of resources into this area struggles to do great things with it but they are having some success). The potential for this technology entrepreneurship is great though, I think, but much more commitment is needed to getting lots of internet and other high technology jobs.
Working in cooperation with Singapore companies could be a win-win for both especially in medical and other high technology areas (as well as finance and also maybe manufacturing).
Some manufacturing is good, I don't see it becoming a huge employer in Johor (but it does provide good jobs - getting some of it in the mix is good. Oil and gas (including palm oil and refining) is also good but again somewhat limited I believe. And you have to worry about the environment being compromised by greedy businesses if the government isn't a strong watchdog - China obviously shows this risk. Shipping/logistics could be a big deal but I don't know realistically if competing with Singapore is likely to be successful in this area.