First, we need to establish: under what premise is the car being provided? Sometimes, "company car" indicates a vehicle provided by the employer, strictly for performing job duties. Other times, the same phrase can mean a vehicle that is provided for job duties, plus for the employee's personal use, as part of a compensation package.
This is a significant difference in terms of answering your question, because it gives us the terms against which you would decide if (or how) to negotiate the specifics. If you're being provided a vehicle strictly to perform your job, you don't really have much ground on which to negotiate for a "nice" vehicle. The employer is basically responsible for providing a vehicle that gives you the transportation you need, and engine size or fancy options aren't really going to come into play (because as has been pointed out in comments, you can get from A to B with a basic car the same as with a fancy one). If, however, the vehicle is provided for personal use, as part of your compensation package, then you and the employer need to agree on the terms under which the vehicle is selected and provided, the same as any other type of compensation - vacation days, salary, etc.
In the question, you stated,
The company gives each employee a company car which can be used for both business and personal matters
So, it's your impression that the vehicle falls under your compensation package, and is not strictly provided for job duties. This means it's up for negotiation and/or should be stipulated under a job contract the same as any other form of compensation.
Which raises the question: Does the vehicle provided count as "acceptable" compensation? When it comes to other forms of compensation, this is more straightforward: You agree on a specific number for salary, and it's obvious if you're getting that number or not. You agree on a certain number of vacation days, and that's the number you're getting. This makes it easy to negotiate: you can work with the employer on what the number is. It also makes it easy to validate: you look at your paycheck and you know if they gave you the right salary or not.
For a vehicle, it's less clear. At least, it's less clear based on the information you've provided. You stated,
A new employee starts with a basic car, but after 2 years of working, the company provides the employee a better (larger, more options, better engine,...) car.
It's hard to decode this statement you've made. Is it written into your contract or job offer that you get a specific vehicle after 2 years? Is it written that you get a specific value (ie a vehicle that has an MSRP of $X)? A vehicle with a specific monthly lease payment? ($X per month)? Or is that just an informal agreement that has no specific definition?
Let's get back to your question:
Would it be a good idea/reasonable to ask for compensation for the cheaper car? (For example by raising my salary.)
The best way for us to answer your question will depend on those factors:
If there's an agreement that states you get a specific vehicle, defined a certain way, after 2 years, then this becomes easy: you can point that out and negotiate appropriately. Ask for a raise based on the discrepancy, or ask for a better vehicle. But based on the fact that you're asking here, I'm assuming that's not the case.
So: the real problem appears to be, there's a component of your compensation for which you have no specific definition. You think you were supposed to get a specific vehicle, the employer is giving you one based on what they think you're supposed to get. You're defining value as the MSRP, the employer is defining it based on the lease cost.
It's very common for vehicles with vastly different MSRPs to lease for the same monthly payment based on other factors (residual value, differences in interest rates, mileage included, brand or dealer promotions only good for a certain timeframe, etc). So it's no surprise that your definition of value is different than the employer's.
You've already pointed this discrepancy out to the employer, and they explained it - the lease cost determines the car you get. I don't think you pointing it out was unreasonable, but you've already had an answer. At this point, since there is apparently no formal definition of the value of the vehicle as part of your compensation, and the employer has explained how they determine the value, there's not much on which to base your argument for additional compensation. "would it be a good idea" or "what do you think I should do" questions don't really fit the Stack Exchange model well, but in this case, it seems pretty clear that it would not be a good idea to push the issue further, unless you have some grounds on which to do that which you haven't mentioned here.