I astonished that you've been able to get to anything close to 60,000 uniques per day on a simple webhosting (shared, right?) account. When I got to 12,000 it damn near locked-up my shared hosting account.
The separate management company will be proactively managing your server. You've not done this before, so its easy to not understand what you are getting into. Your hosting company is primarily concerned with keeping the boxes healthy and the bandwidth up. If they offer server management, its not going to be that great unless you go with one of the real premium companies like RackSpace or something, and they are a lot more expensive. You need someone that is going to be staying on top of the latest updates for Linux and Cpanel and not having you be the guinnea pig for every bug that is found. I've lived it, and it ain't fun. And MOST importantly, you want someone that will keep your server secure. And, last but not least, you want someone that will quickly respond to any problems and fix them for you. I use TouchSupport and have for about 3 years. They are excellent. They know Cpanel well and will keep it updated as it should be. They will also help you with migrating accounts and pretty much anything you need done other than programming issues. Plus, with the two separate companies dealing with your stuff, you can't get jerked around. If one of them is telling you something you don't think is right, you can always bounce it off the other. They both need to do their part correctly or you can easily drop one or the other. If all your eggs are in one basket and you have a serious problem, where do you go for help? Who is going to help you get out of the situation. I've lived through the pain and it can take years off your life. With SoftLayer and TouchSupport you will be able to put your head on the pillow and know what your stuff is covered well. Someone mentioned ServInt. I was with them for a while. I believe you can get a SoftLayer box and TouchSupport combined and not pay anymore than ServInt. My biggest issue with ServInt was that they didn't know squat about Cpanel. When I was with them, I found Cpanel problems by having them, and then they had to find a fix to correct it. With TouchSupport, they know Cpanel and they keep it updated so you never have the problems. If you wanted to run without a control panel, then I think that ServInt would be fine.