Subversion can use the commit-time instead of modification-time if you configure the Subversion client configuration file. (In Unix systems, it's under $HOME/.subversion/config).
I don't believe there's an equivalent one in Git. This was discussed before in Stackoverflow. The big complaint is that this would break Make which is true, but most version control systems do give you that option.
If this is for your company and not for personal use, you might want to look at Perforce. Perforce is a proprietary tool which costs money. There are exceptions: Small projects (no more than two users) and open source projects can use the tool for free.
The big advantage of Perforce is that it allows you to overlay directory structures. For example, you might have a default structure for your server, but each server modifies that structure a bit. You could keep the default one in one directory, and the custom changes for each separate server in another directory. When you do your checkout, you create a view that will combine the two. It's a bit hard to explain, but I found it great for tracking multiple server configurations.
The downsides of Perforce (besides the cost) is that it's more complex than Subversion. In Subversion, you can simply checkout a directory. In Perforce, you create a view of what you want to checkout, then check it out. That means learning the view configuration language. Perforce also has fewer plugins into third party tools than Subversion because it's not as popular. However, it might be good in your situation.
