Most items have a set number -- before the Scout update introduced the Sandman, no item went higher than level 10.
About the time of the Spy / Sniper update, there was a glitch in the random drop system, and normal weapons (that usually have a fixed level number) were generated with a random level between one and one hundred. This has since been fixed, so if you see, to use one of my own items for example, a level 56 Dead Ringer, that means the item is very old. (And now with the latest patch, you'll never see a non-vintage oddly leveled item)
On the other hand, hats will always have a random level. This means nothing, but certain levels are certainly more valuable for trading, for pure sentimental value. (1, 100, 69, 42, etc.)
The singular exception to all of the above is the new Dueling Badge medal misc item, which actually "levels up" as you kill folks during your duels. A level 100 dueling badge works out to 1000 kills (Might be off a factor of ten) during duels, and likewise the rarity of the badge itself (bronze, silver, gold, platinum) is based on level increment. 0-25,26-50,51-75,76-99,100, etc.
In no case does the level of an item have any effect on gameplay.
From the tf2 wiki:
"While it has always been perceived
that each weapon has an equal chance
of being dropped to the player, it
appears that certain weapons that form
part of an item set will drop more
often or less often than others. It is
not known exactly which of these
weapons are rarer or more
common.1"
It mentions that in the old system the drop rate for hats was 1 in 28, but it doesn't mention any changes in the current system.
Best Answer
The official wiki contains no mention of altered drop rates in Mann Up, or any other mode. The current item drop system uses time to determine when to drop an item at regular intervals between 30 and 70 minutes (50 minutes on average), generally after you die.