To answer this question you really need to start with a few questions of what you plan to fish for most, and which fishing technique you prefer to employ.
If you plan on heading North to catch the Pike of your dreams then braided fishing line may be the best option for you. Braided fishing line has no memory, which means less casting tangles than monofilament fishing line. Braided also has 0 stretch and is tougher to cut, leading to a higher quality hook set and less worries of line breaks.
When fishing Lake Trout and choosing which type of line to use it really comes down to technique. Trolling for lakers your best bet is to stick with mono. This is a case where the stretch available in the line actually comes to your advantage. As the boat is trolling forward and setting the hook into the fish at the same time, the force of the hookset it multiplied. The monofilament stretch ensures that the hook is not ripped out of the mouth.
Jigging lake trout generally requires a sharp hard hookset, meaning braided fishing line is really your best choice, but if you only have once choice for your Trout set-up then stick with monofilament fishing line in my opinion.
Fishing for Grayling you could go either way, but I find the weight of the monofilament line helps when casting very small jigs or spinners when compared to the ultralight braid. Also in fast moving current I like the stretch that mono gives when setting the hook.
Lastly, personal preference also plays a huge factor in determining if you spool you reels with mono or braid. If you like the feel of braid, then use it! - Matt