A great dilema.Many people fall in this.
There are 3 issues:
1.Switch to Managerial Job.
3.Product or Service.
The first two issues are most mutually exlcusive.Coz in a managerial pos generally u have to handle more than on projects.Thats why onsite oppurtunity fails.U may get some of em but very less.
If u want to go for onsite better u stick to ur technical and try to opt for some companies like satyam,infosys , patni.They are big players for onsite oppurtunity.
As u want to change the JOB product company will provide u the oppurunity to research and innovation and experiment which u at times will not get in service based industry.But Onsite u will not get and also managerial job will be very demanding in devotion ,time and years of exp.
My answer is
Opt for company(preferably service company) which is willing to pay u and will send u onsite.That way u will gain oniste oppurtunity ,growth in technical skills and good client interaction.After getting back u will have good reason to opt for managerial job.Work over there and then move to Product company u want.
No solution for all ur needs I can find.It may happen that u may find .Look after that
All the best